What is m∠PQR?

The PS is line segment. Q is the point between segments PS. QR is another line segment passes through segment PS. The angle PQR is (3x + 5) degree and angle SQR is (x + 3) degree.

Answer: m∠PQR = 134°

Step-by-step explanation:

Given:  PS is line segment. Q is the point between segment PS. QR is another line segment passes through segment PS.

That means ∠PQR and ∠SQR are linear pair  [Linear pair is a pair of two angles made on one line and their sum is 180°]

⇒  ∠PQR +  ∠SQR  = 180°  (i)

Since, ∠PQR is (3x + 5)° and ∠ SQR is (x + 3)°   [given]

Put this in (i), we get

(3x + 5)° + (x + 3)° = 180°

⇒ 3x + 5 + x + 3 = 180

⇒ 4 x + 8 = 180

⇒ 4 x = 180-8

⇒ 4 x = 172

Divide both sides by 4

⇒  x= 43

So,  ∠PQR=  (3(43) + 5)° = 134°

Hence, m∠PQR = 134°

The measure of m ∠PQR is 134 degrees.

PS is a line segment.

Q is the point between segment PS.

QR is another line segment that passes through segment PS.

The sum of two angles made on one line is equal to 180 degrees.

[tex]\angle \rm PQR + \angle SQR = 180[/tex]

Where the angle QPR is (3x + 5) degree and angle SQR is (x + 3) degree.

Substitute all the values in the equation

[tex]\angle \rm PQR + \angle SQR = 180\\\\(3x+5) + (x+3) =180\\\\3x+5+x+3=180\\\\4x+8=180\\\\4x=180-8\\\\4x=172\\\\x = \dfrac{172}{4}\\\\x =43[/tex]

The value of x is 43 degrees.

Therefore,

The measure of m ∠PQR is;

[tex]\rm m \angle PQR = 3x+5 = 3(43) + 5= 129+5=134[/tex]

Hence, the measure of m ∠PQR is 134 degrees.

To know more about the Properties of triangles click the link given below.

https://brainly.com/question/9404288

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