Question

M angle PQS= 3x; m angle SQR=5x-20 Find x

Answer 1

Let as consider the complete ques is : Ray QS bisects ∠PQR. Solve for x and find m∠PQR. m∠PQS = 3x ; m∠SQR = 5x-20.

Given:

Ray QS bisects ∠PQR.

m∠PQS = 3x

m∠SQR = 5x-20

To find:

The value of x and m∠PQR

Solution:

Ray QS bisects ∠PQR. So,

$m\angle PQS=m\angle SQR$

$3x=5x-20$

$3x-5x=-20$

$-2x=-20$

$x=10$

The value of x is 10.

Now,

$m\angle PQR=m\angle PQS+m\angle SQR$

$m\angle PQR=3x+5x-20$

$m\angle PQR=8x-20$

Put x=10,

$m\angle PQR=8(10)-20$

$m\angle PQR=80-20$

$m\angle PQR=60$

Therefore, the m∠PQR is 60 degrees.