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Ivahew [28]
1 year ago
9

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

Mathematics
2 answers:
Kazeer [188]1 year ago
6 0

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

Lisa [10]1 year ago
3 0

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°

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