P is on the locus of points equidiatant from two given points X and Y. UV is a straight line throuh Y parallel to the locus. If < PYU is 40°, find < XPY.
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You gave an answer in your solvings but u picked another option n I had to fail it
Acording to ChatGPT, it's 70.
Let's call the point where UV intersects the locus point Z. Since UV is parallel to the locus, angle YZU is also 40°.
Since P is equidistant from X and Y, triangle XPY is isosceles. Therefore, angle XPY is equal to angle YPX.
Since triangle PYU is isosceles (angles YUP and YPU are equal), we know that angle PYU is equal to angle PUY. Therefore, angle PYU is 70°.
Since YZU is 40°, ZYP is 70°, and XPY is a straight line, angle XPY = 70°.
Therefore, angle XPY is 70°.
