Question

find the x is qs bisects pqr and pqr=82

Answer 1

Answer:

$x=4$

Step-by-step explanation:

We have been given that ray QS bisects angle PQR  and measure of angle PQR is 82 degrees. We are asked to find the value of x for our given diagram.

Since ray QS bisects angle PQR, so measure of each angle formed by ray QS will be half the measure of angle PQR.

$m\angle PQS=\frac{m\angle PQR}{2}$

$10x+1=\frac{82}{2}$

$10x+1=41$

$10x+1-1=41-1$

$10x=40$

$\frac{10x}{10}=\frac{40}{10}$

$x=4$

Therefore, the value of x is 4.

Answer 2

The value of x is 4 if QS bisects <PQR and <PQR = 82degrees

The line that bisects an angle divides the angle into two equal part.

If QS bisects <PQR as shown in the diagram, hence:

• <PQS = <SQR
• <PQR = 2<PQS

Given the following parameters:

<PQS = 10x+ 1

<PQR = 82degrees

Substitute the given expressions into the formula as shown:

Recall that:

<PQR = 2<PQS

82= 2(10x+1)

82 = 20x + 2

20x = 82 - 2

20x = 80

x = 80/20

x = 4

Hence the value of x is 4 if QS bisects <PQR and <PQR = 82degrees

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