(a) A pentagon ABCDE has sides AE and CD parallel and the line EC
is parallel to side AB. Sides ED and BC, when extended, meet at a
point F. ZABC is equal to ZCDE. Show that ZAEC = ZCFD.
(b) If, furthermore, triangles EDC and DFC are both isosceles, with
ED = DC and DF = FC, find the angles of the pentagon.
Answers
(a) ∠AEC = ∠CFD, by transitive property of equality
(b) ∠CDE = 108°, ∠DCB = 108°, ∠ABC = 108°,∠EAB = 144°, ∠AED = 72°
The reason the above values are correct is as follows:
(a) The given parameters are;
Figure ABCDE is a pentagon
The sides AE is parallel to side CD
Line EC is parallel to side BC
The point of intersection of the extension off side ED and BC = Point F
∠ABC = ∠CDE
Required:
To show that ∠AEC = ∠CFD
Method:
Draw the pentagon ABCDE and include the added construction
Analyze the drawing
Solution:
∠ECF and ∠ABC are corresponding angles between parallel lines EC ║BC
∴ ∠ECF ≅ ∠ABC by corresponding angles formed by parallel lines are congruent
∠ECF = ∠ABC by definition of congruency
∠ABC = ∠CDE = ∠ECF by transitive property
∠ECD ≅ ∠AEC by alternate angles formed between parallel lines having a common transversal
∠ECD = ∠AEC by definition of congruency
∠ECF = ∠FCD + ∠ECD by angle addition postulate
∠CDE = ∠FCD + ∠CFD by exterior angle theorem
From ∠CDE = ∠ECF above, we have;
∠ECF = ∠FCD + ∠ECD = ∠FCD + ∠CFD
∴ ∠ECD = ∠CFD by addition property
∠ECD = ∠AEC, therefore;
∠AEC = ∠CFD, by transitive property
(b) Given that ΔEDC and ΔDFC are both isosceles triangles, with sides;
ED = DC, and DF = FC;
Let r represent ∠CFD, we have;
∠FCD = ∠CDF by base angles of isosceles triangle ΔDFC
∠ECD = ∠CED by base angles of isosceles triangle ΔEDC
∠AEG = ∠CDE by corresponding angles formed by parallel lines having a common transversal
∠AEC = ∠ECD by alternate angles
∴ ∠AEG + ∠AEC + ∠CED = 180° Sum of angles on a straight line
∠CDE = ∠CFD + ∠FCD
∠CDE + ∠CDF = 180° (linear pair angles)
∴ ∠AEG + ∠CDF = 180° by transitive property
∠AEC + ∠CED = ∠CDF by transitive property
∠AEC = ∠ECD = ∠CED = ∠CFD = r
∴ ∠CFD + ∠CFD = ∠CDF
2·r = ∠CDF
∠CDE = ∠FCD + ∠CFD
∠FCD = ∠CDF = 2·r
∴ ∠CDE = 2·r + r = 3·r
∠CDE = 3·r
The angles of the pentagon are;
∠CDE + ∠DCB + ∠ABC + ∠EAB + ∠AED = 540° sum of angles in a pentagon
∠DCB = 180° - ∠FCD
∠DCB = 180° - 2·r
∠ABC = ∠CDE = 3·r
∠EAB = ∠CEH corresponding angles
∠CEH = 180 - ∠AEC
∴ ∠EAB = 180° - ∠AEC
∴ ∠EAB = 180° - r
∠AED = ∠AEC + ∠CED = r + r = 2·r
∠AED = 2·r
Therefore, we have;
3·r + 180° - 2·r + 3·r + 180° - r + 2·r = 540°
5·r + 360° = 540°
r = (540° - 360°)/5 = 36°
r = 36°
∠CDE = 3 × 36° = 108°
∠DCB = 180° - 2×36° = 108°
∠ABC = 3 × 36° = 108°
∠EAB = 180° - 36° = 144°
∠AED = 2 × 36° = 72°
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Related Questions
A sequence of transformations is described below.
A dilation about a point P
A rotation about another point Q
A vertical stretch about the horizontal line PQ
A reflection over a line PQ
Here is the answer-
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This sequence includes a vertical stretch, which is neither a rigid transformation nor a dilation.
Answers
Answer:
I don't understand this
What is –70 divided by 700
PLZ HELP ME!!!
Answers
Answer: -0.1
Step-by-step explanation: Calculator
Hello!
-70 : 700 = -0,1 → answer
Good luck! :)
How would I write this equation? Looking for an answer ASAP.
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Step-by-step explanation:
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The second number in an ordered pair of numbers that corresponds to a point on a coordinate system is the
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Answers
Answer:
y value
Step-by-step explanation:
when you write an ordered pair the first number is your x and the second number is your y. these make a point on a graph.
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Answer:
a
Step-by-step explanation:
Emilio compro 3 bolitas y pago 180 en total. Carlos compro 4 bolitas y pago 200 en total ¿Quién pago menos por cada una de las bolitas que compro?
Answers
Answer:
emilio:
3 bolitas = 180
1 bolita = 60
carlos:
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How many solutions are there to the equation below? 9(x – 4) = 9x – 33
Answers
Answer:
no solution
Step-by-step explanation:
Please Help
cube root√(a+b)^-7 * (a+b)^1/3
I have also send photo of question please check
Answers
[tex]\sf\huge\underline\red{SOLUTION:}[/tex]
[tex]\sf\rightarrow \sqrt[3]{ {(a + b)}^{ - 7} } \times {(a + b)}^{ \frac{1}{3} } [/tex][tex] \\ \rightarrow\sf {(a + b)}^{ \frac{ - 7}{3} } {(a + b)}^{ \frac{1}{ 3 } } [/tex][tex] \\ \rightarrow\sf {(a + b)}^{ - \frac{7}{3} } {(a + b)}^{ \frac{1}{3} } [/tex][tex] \\ \rightarrow\sf {(a + b)}^{ - \frac{7}{3} + \frac{1}{3} } [/tex][tex] \\ \rightarrow\sf {(a + b)}^{ \frac{ - 7 + 1}{3} } [/tex][tex] \\ \rightarrow\sf {(a + b)}^{ \frac{ - 6}{3} } [/tex][tex] \\ \rightarrow\sf {(a + b)}^{ \frac{3 - 2}{3} } [/tex][tex] \\ \rightarrow\sf {(a + b)}^{ \frac{3 \times - 2}{3(1)} } [/tex][tex] \\ \rightarrow\sf {(a + b)}^{ \frac{3 \times - 2}{3 \times 1} } [/tex][tex] \\ \rightarrow\sf {(a + b)}^{ \frac{ - 2}{1} } [/tex][tex]\rightarrow\sf {(a + b)}^{ - 2} [/tex][tex]\red\rightarrow\large\boxed{\sf{\red{ \frac{1}{ {(a + b)}^{2} } }}}[/tex][tex]\sf\huge\underline\red{ANSWER:}[/tex]
[tex]\red\rightarrow\large\boxed{\sf{\red{ \frac{1}{ {(a + b)}^{2} } }}}[/tex]✍︎☘︎ᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴ☘︎
✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ
Answer:
ハハハハハハハバカあなたも答えがわからない質問でも簡単に黙ってバカバカバカバカゴッド
How many solutions does the nonlinear system of equations graphed below
have?
• A. One
• B. Two
• C. Four
O D. Zero
SUBMIT
Answers
Multiple choice please help!!
Answers
3 and 4
Step-by-step explanation:
y=5x
y=5(0)
y=0
y=5x
y=5(10)
y=50
y=5x
y=5(51)
y=255
y=5x
y=5(400)
y=2000
The graph below have the same shape. What is the equation of the graph?
Answers
Answer:
C
Step-by-step explanation:
The graph has been translated down 4 units and moved to the right 2 units
so correct answer is C (x-2)^2-4.
The sum of the angles of all the sectors in a pie chart should add up to ???
a). 180⁰
b). 90⁰
c). 360⁰
Answer me please ...
Answers
Answer:
C
Step-by-step explanation:
Since the sectors all meet at the centre of the circle, then
The angles around a point sum to 360° → A
90°... See More
https//90°.com
What number is increased by 40% become 28?
a.5 b. 10 c. 15 d. 20
Answers
Answer:
d. 20
Step-by-step explanation:
28 ÷ (100%+40%)
= 28 ÷ 140%
= 28 ÷ 1.4 = 20
Answer:
option d
Step-by-step explanation:
Let the number be x
40% of x = 0.40x
Increased by 40% = 28
That is ,
x + 0.40x = 28
1.40x = 28
[tex]x = \frac{28}{1.40}\\[/tex]
[tex]x = \frac{28 \times 100}{1.40 \times 100 } = \frac{28 \times 100}{140} =\frac{4 \times 100}{20} = 4 \times 5 = 20[/tex]
Therefore, the number is 20
What is the value of x?
Enter your answer in the box.
Answers
what is the length of KM ? NO LINKS .
Answers
Answer:
80 units
Step-by-step explanation:
KN = MN
9x - 5 = 7x + 7
2x = 12
x = 6
KM = 2KL
KM = 2(6x + 4)
KM = 12x + 8
KM = 12(6) + 8
KM = 80
Answer:
80
Step-by-step explanation:
which of the following functions is graphed below?
Answers
Answer:
d number on is the wright answer
hope it may help you
PLEASE HELP ME SOMEONE I NEEDDDDDDD HELP PLEASE QUICK!!!!!!!!
Answers
Answer:
2/60 = 1/30 = 3.3%
Step-by-step explanation:
help! urgent asap!!!!!!!!!!
Answers
Answer:
A
Step-by-step explanation:
This is because the answer you picked means congruent to, however these two triangles are not the same size
You offer to sell a used car for $1,895. Yesterday you purchased the car for $1,755. What percentage markup on cost are you charging (to the nearest tenth)?
Answers
Answer:
8.0%
Step-by-step explanation:
1. [tex]1895-1755=140[/tex]
2.[tex]\frac{140}{1755} =0.07977208[/tex]
3. 8.0%
What is the domain and range of graph!!! 10 points!!!
Answers
Answer:
THIRD OPTION - Domain: (0, infinity)
Range: (-infinity, + infinity)
Step-by-step explanation:
The graph is an asymptote, therefore the domain must start at 0 and end at infinity. The range is all real numbers because eventually it will reach all y values.
Last month, a factory produced 880 television sets. This month, the same factory produced 1,210 television sets. The increase in production from last month to this month is
Answers
Answer:
330 television set
Step-by-step explanation:
Last month production = 880 television sets
This month production = 1,210 television sets
The increase in production from last month to this month = This month production - Last month production
= 1,210 - 880
= 330
The increase in production from last month to this month = 330 television set
As per linear equation, the increase in production of television of the factory is 330.
What is a linear equation?A linear equation is an equation where the variable has the highest power of 1.
Given, a factory produced 880 television sets last month.
This month, the same factory produced 1,210 television sets.
Therefore, the increase in production of television of the factory is
[tex]= (1210-880)\\= 330[/tex]
Learn more about a linear equation here: https://brainly.com/question/11203335
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HELP I AM TIMED. Determine whether the equation is an identity or not an identity.
Answers
Answer:
It is not an identityStep-by-step explanation:
There are 10 common trig identities which I am aware of.
Some are in the image attached
The first image is known as b
Basic Identities
The second are known as Trigonometric / Pythagorean Identities .
The third : Co-function identities
and many more.
I'm only allowed to post five images so that's all I have.
Help me out please thanks
Answers
Answer:
1.5 is the correct answer
Step-by-step explanation:
The time it four hours. In those 4 hours the temperature changer by 6 degrees. So 6 divided by 4 is 1.5.
Answer: Choice D is correct. The slope is 1.5
This means that for every hour, the temperature is increasing by 1.5 degrees Fahrenheit.
=======================================================
Work Shown:
slope = rise/run
slope = (change in y)/(change in x)
slope = (change in temperature)/(change in time)
slope = 6/4 .... see note below
slope = 3/2
slope = 1.5
note: The 6 refers to the jump from -2 to 4; the denominator 4 represents the amount of elapsed time from 8 AM to 12 PM
Which method is used in elimination to find the solutions of a - b = 9 and a + b = 5?
Answers
The substitution method is used in elimination to find the solution to the equation.
What is the system of two equations?A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.
The given equation in the problem is;
Equation P: a - b = 9
Equation Q: a+b=5
The value obtained from the equation P is;
a - b = 9
a=b+9
Substitute the value in the equation Q;
a+b=5
b+9+b=5
2b=9-5
b=2
The value of a is;
a-b=9
a-2=9
a=9+2
a=11
Hence the value of a and b will be 11 and 2.
To learn more about the system of two equations, refer to the link;
https://brainly.com/question/21620502
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6. Write an equation of a line that is Parallel to the line: y = 3x -3
Answers
Answer:
3x - y -6 = 0
Step-by-step explanation:
We need to find the Equation of the line parallel to the given equation of line . The given equation of the line is ,
[tex]\rm\implies y = 3x - 3 [/tex]
Slope Intercept Form :-
[tex]\rm\implies y = mx + c [/tex]
where ,
m is slopec is y intercept .Therefore , the Slope of the line is 3 . Let the parallel line passes through ( 3,3) . We know that the parallel lines have same slope . Therefore the slope of the parallel line will also be 3 .
Using point slope form :-
[tex]\rm\implies y - y_1 = m ( x - x_1) \\\\\rm\implies y - 3 = 3( x - 3 ) \\\\\rm\implies y -3 = 3x -9 \\\\\rm\implies 3x -y -9+3=0\\\\\rm\implies \boxed{\rm\red{ 3x -y -6=0}}[/tex]
Is the graph increasing, decreasing, or constant?
Answers
Answer:
it's increasing.
Step-by-step explanation:
I'm not sure what else write here, it's obvious it's increasing
Answer:
Increasing
Step-by-step explanation:
You can see the line moving up on the graph starting from its origin (0,0) then moving to (1,1) then moving slowly up then finally ending at (12,3).
which eqation represents the line that passes through (-6, 7) and (-3, 6)
Answers
Answer:
The answer is y= - ⅓x + 5 in slope intercept form and y-7 = - ⅓ (x + 6) in point slope form.
please answer asap ------------------ ------------------ ------------------ ------------------
Answers
Answer:
Answer :
It's 3v - 9/2
Step-by-step explanation:
....
Janna is using a cone-shaped cup to fill a cylindrical container. The cup has the same height and radius as the container. How many rimes will she have to fill the cone-shaped cup to completely fill the cylindrical container.
Answers
Answer:
3 times
Step-by-step explanation:
Step 1: Express the volume of the cup in terms of "r" (radius) and "h" (height)
The formula for the volume of a cone is:
Vcone = 1/3 × h × π × r²
Step 2: Express the volume of the container in terms of "r" and "h"
The formula for the volume of a cylinder is:
Vcylinder = h × π × r²
Step 3: Calculate how many times the volume of the cone is contained in the volume of the cylinder
Vcylinder/Vcone = (h × π × r²) / (1/3 × h × π × r²) = 3
X
2
4
00
12
V
4
2.
1
2/3
Answers
Answer:
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5
Step-by-step explanation:
Select the correct answer.
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table
A regular six sided die and an eight equal segment spinner, numbered 1 to 8, are rolled/spun simultaneously. What are the odds in favor of spinning a prime number on the spinner and rolling a number less or equal to 4 on the die?
Answers
Answer:
1/3
Step-by-step explanation:
In statistics, the probability of both an event A and an event B happening is equal to the probability of A happening multiplied by the probability of event B happening.
Let's say spinning a prime number is event A and rolling a number ≤ 4 is event B.
There are 8 possibilities on an eight equal segment spinner, and there are 4 prime numbers between 1 and 8 (including 8), which are 2, 3, 5, and 7. This means that the probability of spinning a prime number is 4/8, or 1/2
There are 6 possibilities on a die, and there are 4 possibilities of rolling a 4 or less (1, 2, 3, 4). Therefore, the probability of rolling 4 or less on a die is 4/6, or 2/3
The probability of both of these happening can be calculated by multiplying these together, so 1/2 * 2/3 = 2/6 = 1/3