Question

If QS bisects PQR and measure angle PQR is 82 degrees, find the value of x.

a) 41
b) 164
c) 82
d) 123

Answer 1

By bisecting ∠PQR with QS and knowing that the total angle is 82 degrees, each of the two resulting angles is 41 degrees, which gives us the value of x as 41 degrees.

Step-by-step explanation:

If QS bisects ∠PQR and the measure of ∠PQR is 82 degrees, we need to find the value of x given the fact that a bisection means dividing an angle into two equal parts. Since QS bisects ∠PQR, ∠PQS and ∠QSR will both be equal angles. Hence, we can set up the equation x + x = 82 degrees.

Combining like terms, we get 2x = 82 degrees. Dividing both sides by 2 to solve for x gives us x = 41 degrees. Therefore, the value of x, which represents the measure of ∠PQS and ∠QSR, is 41 degrees.