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

The measure of angle R is 20°.

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°.