Question

Geometry: Line QS bisects angle PQR. Solve for x and find the measure of angle PQR.
(actual problem:) the measure of angle PQS=2x + 1; the measure of angle RQS = 4x - 15.

Answer 1

It is given in the question that,

Line QS bisects angle PQR. Solve for x and find the measure of angle PQR.

And

$m \angle PQS = 2x+1 \\ m \angle RQS = 4x-15$

Since QS bisects angle PQR, therefore

$m \angle PQS = m \angle RQS$

Substituting the values, we will get

$2x+1=4x-15 \\ 1+15 = 4x-2x \\ 2x = 16 \\ x = 8$

Answer 2

Answer:

x = 8

∠PQR = 34°

Step-by-step explanation:

Given: Line QS bisects ∠PQR

• The measure of ∠PQS = 2x + 1
• The measure of ∠RQS = 4x - 15

QS is bisector of ∠PQR

So, ∠PQS = ∠RQS

2x + 1 = 4x - 15

4x - 2x = 1 + 15

     2x = 16

      x = 8

∠PQS = 2(8) + 1

          = 16+1

         = 17°

∠RQS = 4x-15

          = 4(8)-15

          = 17°

∠PQR = ∠PQS + ∠RQS

          = 17° + 17°

          = 34°

Hence, The measure of ∠PQR is 34°