Question

In the triangles, XY = MP and YZ = PN. Triangles Y X Z and P M N are shown. The length of side X Z is 23 inches. The length of side M N is 19 inches. Sides X Y and M P are congruent. Sides Y Z and P N are congruent. If mAngleP = 85°, which is a possible measure for AngleY? mAngleY = 80° mAngleY = 85° mAngleY = 100° mAngleY = 180°

Answer 1

I believe the correct answer would be m<Y= 100° which would be letter C.

Explanation:

Answer 2

`m\angle Y = 85\°`

Explanation:

In Triangles YXZ and PMN

`XY \cong MP\\YZ \cong PN`

Since the third side of triangle subtended by two congruent sides will always be congruent, the two triangles are congruent by SSS congruence theorem.

Therefore:
`\triangle XYZ \cong \triangle MPN\\`

If the measure of angle P = 85°

Since P and Y are in the same positions(as seen in the diagram) in the two triangles respectively, the measure of angle Y is also 85 degrees.