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? 20 75 85 160

Answer 1

I think the answer is going to be 20

Answer 2

Answer:

The measure of angle R is 20°.

Step-by-step explanation:

Since, We know that,

When two triangles are similar then their corresponding angles are congruent or the measures of corresponding angles are equal,

In triangles MNO and PQR,

Angles M, N and O are corresponding to angles P, Q and R.

Given,

$\triangle MNO\sim \triangle PQR$

$m\angle N=85^{\circ}$

$m\angle P=75^{\circ}$

Also, By the above property,

$m\angle N = m\angle Q$

$\implies m\angle Q = 85^{\circ}$

Now, the sum of all interior angles of a triangle is supplementary,

So, in ΔPQR,

$m\angle P+m\angle Q+m\angle R= 180^{\circ}$

$75^{\circ}+ 85^{\circ}+m\angle R= 180^{\circ}$

$160^{\circ}+m\angle R= 180^{\circ}$

$\implies m\angle R=20^{\circ}$

Hence, the measure of angle R is 20°.