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 mAngle P = 85°, which is a possible measure for Angle Y?


mAngleY = 80°

mAngleY = 85°

mAngleY = 100°

mAngleY = 180°

Answer 1

C.m angle Y=100 degree

Explanation:

We are given that

In triangle XYZ and MPN

XY=MP

YZ=PN

XZ=23 in

MN=19 in

`m\angleP=85^(\circ)`

23 in>19 in

XZ>MN

Opposite angle of side XZ=Angle Y

Opposite angle of side MN=Angle P

We know that

When a side is greater than other side

Then, the angle opposite to greater side will be greater than the angle opposite to smaller side.

Ange Y>angle P

Option A and B are wrong

Option D is not possible because triangle angle sum =180 degree

Therefore, m angle Y=100 degree

Answer 2

Option C.

Explanation:

Given information: XY ≅ MP, YZ ≅ PN , XZ=23 inches and MN=19 inches.

In triangles YXZ and PMN,

XY ≅ MP (Given)

YZ ≅ PN (Given)

Included angle of the first triangle is ∠Y.

Included angle of the second triangle is ∠P=85.

According to hinge theorem if two sides of a triangle are congruent to two sides of another triangle, then third side depends on the included angle.

If the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

XZ > MN

∠Y > ∠P

∠Y > 85°

Interior angle of a triangle is always less than 180°, because the sum of all interior angles of a triangle is 180°.

Only possible value of ∠Y is 100°.

Therefore, the correct option is C.