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1 year ago

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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Kindly refer to the attached image.

$\triangle ABC$ represents the 1st angle of elevation of sun i.e. 58°

$\triangle ABD$ represents the 2nd angle of elevation of sun i.e. 36°

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