Question

Ray YW is the angle bisector of ∠XYZ. If m∠XYW = 32°, what is m∠XYZ?

a) 32°
b) 64°
c) 128°
d) 16°

Answer 1

The angle bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. In this case, since we are given that angle XYW measures 32°, we can substitute this information into the equation and solve for m∠XYZ.

Step-by-step explanation:

The angle bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. In this case, ray YW bisects angle XYZ. So, by applying the angle bisector theorem, we can set up the proportion (XY / XW) = (YZ / YW). Since we are given that angle XYW measures 32°, we can substitute this information into the equation and solve for m∠XYZ. (XY / XW) = (YZ / YW) => (XY / XW) = (YZ / YW) => XY * YW = YZ * XW => 32 * YW = YZ * XW. Since Ray YW is an angle bisector, we can assume that XY = XW and therefore, the equation becomes 32 * XY = YZ * XY => 32 = YZ. So, m∠XYZ = 32°. Therefore, the answer is option a) 32°.