Question

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

a. 6
b. 17
c. 90
d. 102

Answer 1

To find the value of m, we can use the angle bisector theorem to determine that the ratio of zx/wx is equal to the ratio of yx/xy. By setting this expression equal to the measure of yxz, we can solve for m.

Step-by-step explanation:

To find the value of m, we need to use the properties of angles in a triangle. Since z x bisects ∠wzy, we can use the angle bisector theorem to determine that the ratio of z x to wx is equal to the ratio of y x to xy.

Therefore, we have the equation zx/wx = yx/xy. Since wz = xy (given), we can substitute and simplify the equation to:
zx/wx = yx/wz = yx/xy

Since we are given that the measure of ∠yxz is (6m - 12)°, we can set this expression equal to zx/wx and solve for m.

(6m - 12)° = yxz
(6m - 12)° = zx/wx

Simplifying the equation:
(6m - 12)° = yx/wz
(6m - 12)° = wx/xy

Since wz = xy, we can rewrite the equation as:
(6m - 12)° = wx/yz

Therefore, m = 17 (Option b)