The deck that Amos is building is in the shape of a parallelogram, DGRY. The measure of

Answers

Answer 1

Complete Question:

The deck that Amos is building is in the shape of a parallelogram, DGRY.  The measure of D is five-halves the measure of Y. Find the measure of  each angle of the deck.

Answer:

[tex]\angle G = \angle Y = 51.43 ^{\circ}[/tex]

[tex]\angle D = \angle R = 128.57 ^{\circ}[/tex]

Step-by-step explanation:

Given

Shape: Parallelogram DGRY

Dimension: [tex]\angle D = \frac{5}{2}\angle Y[/tex]

Required

Find the measure of each angle

D and R are opposite sides & G and Y are also opposite sides.

So, we have:

[tex]\angle D = \angle R = \frac{5}{2}\angle Y[/tex]

and

[tex]\angle G = \angle Y[/tex]

The sum of angles is given as:

[tex]\angle D + \angle G + \angle R + \angle Y=360^{\circ}[/tex]

Substitute values for [tex]\angle D, \angle G \ \& \angle R[/tex]

[tex]\frac{5}{2}\angle Y + \frac{5}{2}\angle Y + \angle Y + \angle Y = 360^{\circ}[/tex]

Take LCM

[tex]\frac{5\angle Y + 5\angle Y + 2\angle Y+ 2\angle Y}{2}= 360^{\circ}[/tex]

[tex]\frac{14\angle Y}{2}= 360^{\circ}[/tex]

Multiply both sides by [tex]\frac{2}{14}[/tex]

[tex]\frac{2}{14} * \frac{14\angle Y}{2}= 360^{\circ} * \frac{2}{14}[/tex]

[tex]\angle Y= 360^{\circ} * \frac{2}{14}[/tex]

[tex]\angle Y= \frac{ 360^{\circ} *2}{14}[/tex]

[tex]\angle Y= \frac{720^{\circ}}{14}[/tex]

[tex]\angle Y= 51.43 ^{\circ}[/tex]

So:

[tex]\angle G = \angle Y = 51.43 ^{\circ}[/tex]

[tex]\angle D = \frac{5}{2}\angle Y[/tex]

[tex]\angle D = \frac{5}{2} * 51.43^{\circ}[/tex]

[tex]\angle D = \frac{5* 51.43^{\circ}}{2}[/tex]

[tex]\angle D = \frac{257.15^{\circ}}{2}[/tex]

[tex]\angle D = 128.57 ^{\circ}[/tex]

Hence:

[tex]\angle D = \angle R = 128.57 ^{\circ}[/tex]


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