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,
[tex]m\angle PQS=m\angle SQR[/tex]
[tex]3x=5x-20[/tex]
[tex]3x-5x=-20[/tex]
[tex]-2x=-20[/tex]
[tex]x=10[/tex]
The value of x is 10.
Now,
[tex]m\angle PQR=m\angle PQS+m\angle SQR[/tex]
[tex]m\angle PQR=3x+5x-20[/tex]
[tex]m\angle PQR=8x-20[/tex]
Put x=10,
[tex]m\angle PQR=8(10)-20[/tex]
[tex]m\angle PQR=80-20[/tex]
[tex]m\angle PQR=60[/tex]
Therefore, the m∠PQR is 60 degrees.
