Question

QS¯¯¯¯¯¯¯ bisects ∠PQR . If m∠PQS = 5x and m∠RQS = 2x + 6, then what is m∠PQR ? m∠PQR is

Answer 1

Answer:

$PQR = 20$

Step-by-step explanation:

Given

Bisector: QS

$PQS = 5x$

$RQS = 2x + 6$

Required

Determine PQR

Since PQR is bisected to PQS and RQS, we have that

$PQS = RQS$

Substitute expressions for PQS and RQS

$5x = 2x + 6$

Collect Like Terms

$5x - 2x = 6$

$3x = 6$

Divide both sides by 3

$x = 2$

Solving for PQR;

$PQR = PQS + RQS$

$PQR = 5x + 2x + 6$

$PQR = 7x + 6$

Substitute 2 for x

$PQR = 7 * 2 + 6$

$PQR = 14 + 6$

$PQR = 20$