Question

If QS bisects PQT, SQT=(8x-25), PQT=(9x+34), and SQR = 112, find each measure

Answer 1

The value of

• x = 12°

• m∠PQS = 71°
• m∠PQT = 142°
• m∠TQR = 41°

Given

SQT = (8x₋25) and PQT = (9x₊34)

SQR = 112°

we need to find the x angle and the remaining angles.

we know that QS bisects ∠PQT

⇒ 2(8x₋25)° = (9x₊34)°

(16x ₋ 30)° =  (9x₊34)°

16x ₋ 9x = 34 ₋ 30

x = 12°

substitute x value in the given values of angles.

m∠PQS = (8x ₋ 25)° = (8(12)₋25) = 71°

m∠PQT = (9(12)₊34) = 142°°

m∠TQR = 112° ₋ ∠PQS = 112° ₋ 71° = 41°

hence we get the desired angles from the given angles.

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