Question

Triangle MNO is similar to triangle PQR if angle N measures 85 degrees and angle P measures 75 degrees what is the measure of angle R?

Answer 1

Since both angles are similar:
P:Since both are similar plug in 75
Q:85
R: 20 ( 75 + 85 = 160 -> 180(the area of triangles) - 160 = 20)

Answer 2

m∠R = 20°

Explanation:

Given that : ΔMNO ≅ ΔPQR

So, By using the property that corresponding parts of congruent triangles are equal.

We get, m∠M = m∠P , m∠N = m∠Q , m∠O = m∠R

Now, m∠N = 85

⇒ m∠N = m∠Q = 85

Also, m∠P = 75

Now, in ΔPQR using angles sum property of a triangle

⇒ m∠P + m∠Q + m∠R = 180

⇒ 75 + 85 + m∠R = 180

⇒ 160 + m∠R = 180

⇒ m∠R = 20°