Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X.
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We have been given that measure of arc WY is 76° and and measure of arc XZ is 112°. We are asked to find the difference of of the measures of angle WPY and angle XPY.
First of all we will find the measure of angle WPY using intersecting secants theorem. Intersecting secants theorem states that measure of angle formed by two intersecting secants inside a circle is half the sum of intercepting arcs.
We can see that angle WPY and angle XPY are linear angles, so they will add up-to 180 degrees.
Now we need to find difference of both angles as:
Therefore, the difference of the measures of angle WPY and angle XPY is 8 degrees.
