Question

Triangle w z y is cut by bisector z x. The lengths of sides z w and z y are congruent. zx bisects ∠wzy. If the measure of ∠yxz is (6m – 12)°, what is the value of m?

1) 6
2) 17
3) 90
4) 102

Answer 1

The value of m can be determined by using the angle bisector theorem and the fact that the lengths of sides ZW and ZY are congruent. We can set up an equation based on the angles in triangle WZY to solve for m.

Step-by-step explanation:

Given that triangle WZY is cut by bisector ZX and the lengths of sides ZW and ZY are congruent, we can determine the value of angle YXZ by using the angle bisector theorem. According to the theorem, the angle bisector divides the opposite side into segments that are proportional to the lengths of the adjacent sides.

Let's assume that the measure of angle YXZ is (6m - 12)°. Since ZX bisects angle WZY, we know that the measure of angle ZXY is equal to the measure of angle YXZ, which is (6m - 12)°. In triangle WZY, the measure of angle Z is equal to the sum of the measures of angles ZXY and YXZ, so angle Z is 2(6m - 12)°.

Since the sum of the angles in a triangle is 180°, we can set up the equation: (6m - 12) + (6m - 12) + 2(6m - 12) = 180°. Solving this equation will give us the value of m.