The measure of angle WXY is 37 degrees, and the measure of angle ZXW is 74 degrees, confirming the angle bisector theorem.
In the given scenario where XY bisects angle WXZ and the measure of angle ZXY is 37 degrees, we can use the angle bisector theorem to determine the measures of angle WXY and ZXW. The theorem states that if a line segment bisects an angle, it divides the opposite side into segments that are proportional to the other two sides of the triangle.
Let the measure of angle WXY be denoted as x and ZXW as y. Since XY bisects angle WXZ, we can set up the proportion:
ZX/ZW = XY/YW
Given that the measure of angle ZXY is 37 degrees, we know that the sum of the measures of WXY and ZXW is 37 degrees. Substituting the measures, the proportion becomes:
ZX/ZW = tan(y)/tan(x)
Solving for x and y, we find x = 37 degrees and y = 74 degrees.
Therefore, the measure of angle WXY is 37 degrees, and the measure of angle ZXW is 74 degrees.
The question probable may be:
XY bisects ∠ WXZ and m∠ ZXY=37°. Find m∠ WXY and m∠ ZXW m∠ WXY=□° m∠ ZXW=□°