Question

In the triangles, XY = MP and YZ = PN.

If mP = 85°, which is a possible measure for Y?

1. mY = 80°
2. mY = 85°
3. mY = 100°
4. mY = 180°

Answer 1

Given that in triangle XYZ and MPN XY=MP, YZ=PN and the ratio of XZ to MN is 23/19.
Thus the possible size of angle Y given that mP=85 will be:
mY/P=23/19
mY/85=23/19
mY=23/19*85
mY=102.9
The approximate value is therefore mY=100

Answer 2

Answer: Option 3. is the right option. 100° is a possible measure for m∠Y.

Explanation:

Given : Two triangles ΔXYZ and ΔMPN where XY = MP and YZ = PN

XY=23 in. and MN=19 in.

Clearly XY>MN

⇒m∠Y>m∠P ...(angle opposite to the greater side is greater )

And m∠P=85° ⇒ m∠Y>85°

So option 1) and option 2) are not correct as they are less than 85°.

Option 4 is also not correct as it cannot be possible in a triangle because 180° is the angle of a straight line.

Therefore, Option 3 should be the correct option correct option, 100° is a possible measure for m∠Y.