If QS−→ bisects ∠PQR, m∠PQS=7x−6, and m∠RQS=4x+15, what is m∠PQR?

Answer 1

An angle bisector cuts an angle in half meaning that the two halves are congruent. If they are congruent, then their measures are the same meaning that "7x−6" must equal "4x+15" so:

7x − 6 = 4x + 15 [add 6 to both sides to get:

7x = 4x + 21 [subtract 4x from both sides to get:

3x = 21 [divide both sides by 3 to get:

x = 7

If x = 7 then the measure of each half (∠PQS or ∠RQS) can be found by plugging "7" into either "7x−6" or "4x+15"

7(7) - 6 = 49 - 6 = 43°.

The measure of ∠PQR is twice that (since each congruent angle is 43°) so m∠PQR = 86°

Answer 2

Set these two equal to each other (bisects means splits evenly into two parts, so that's why they are equal to each other). Solve for X, plug back into one of the equations to see how big 1/2 of the total angle is, then double that!

7x−6 = 4x+15

1. X = 7 plug this back into one of the equations to see one side is 43 degrees, double that for the answer, 86°