Question

Find the value of line segment xy bisects wxz, and mzxy = 41.

a) 41∘
b) 82∘
c) 123∘
d)164∘

Answer 1

Line segment XY bisects angle WXZ into two equal parts. Since one part is 41 degrees, the full angle WXZ is 82 degrees. Thus, the value of angle WXZ is 82 degrees.

Step-by-step explanation:

If line segment XY bisects angle WXZ, and the measure of angle MZXY is given as 41°, we can infer that line segment XY creates two congruent angles when it bisects angle WXZ. Since the angle is bisected, both angles created are equal. Hence, if one of the resulting angles is 41°, the other will also be 41°.

The full measure of angle WXZ would then be the sum of both bisected angles: 41° + 41° = 82°. Therefore, the correct answer is 82°, which corresponds to option b).