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°

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

Step-by-step 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.

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal