Question

Please help me understand this

Answer 1

Answer:

The value of x is 12.

The measure of ∠PQS is 71°.

The measure of ∠PQT is 142°.

The measure of ∠TQR is 41°.

Step-by-step explanation:

Given information: QS bisects ∠PQT, m∠SQT=(8x-25)°, m∠PQT=(9x+34)° and m∠SQR=112°.

QS bisects ∠PQT it means QS divides ∠PQT in two equal parts.

$\angle PQS=\angle SQT$                  .... (1)

$\angle SQT=\frac{1}{2}(\angle PQT)$

$2\angle SQT=\angle PQT$

Substitute the value of each angle.

$2(8x-25)=(9x+34)$

$16x-50=9x+34$

Isolate variable terms.

$16x-9x=50+34$

$7x=84$

Divide both sides by 7.

$x=12$

The value of x is 12.

From equation (1) we get

$\angle PQS=\angle SQT=(8x-25)^{\circ}$

$\angle PQS=(8(12)-25)^{\circ}$

$\angle PQS=71^{\circ}$

The measure of ∠PQS is 71°.

$m∠PQT=(9x+34)^{\circ}$

$m∠PQT=(9(12)+34)^{\circ}$

$m∠PQT=142^{\circ}$

The measure of ∠PQT is 142°.

$m∠TQR=m\angle SQR-m\angle SQT$

$m∠TQR=112^{\circ}-71^{\circ}$

$m∠TQR=41^{\circ}$

The measure of ∠TQR is 41°.

Answer 2

QS bisects <PQT so <PQS = <SQT 
m<SQT = 8x - 25
m<PQT = 9x + 34
m<PQT = 2(m<SQT)
9x + 34 = 2(8x - 25)
9x + 34 = 16x - 50
7x = 84
x = 12

m<SQT = 8(12) - 25 = 71

m<PQS = m<SQT = 71

m<PQT = 2(m<PQS) = 2(71) = 142

m<TQR = m<SQR - m<SQT = 112 - 71 = 41

answer
x = 12
m<PQS = 71
m<PQT = 142
m<TQR = 41