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,
[tex]\triangle MNO\sim \triangle PQR[/tex]
[tex]m\angle N=85^{\circ}[/tex]
[tex]m\angle P=75^{\circ}[/tex]
Also, By the above property,
[tex]m\angle N = m\angle Q[/tex]
[tex]\implies m\angle Q = 85^{\circ}[/tex]
Now, the sum of all interior angles of a triangle is supplementary,
So, in ΔPQR,
[tex]m\angle P+m\angle Q+m\angle R= 180^{\circ}[/tex]
[tex]75^{\circ}+ 85^{\circ}+m\angle R= 180^{\circ}[/tex]
[tex]160^{\circ}+m\angle R= 180^{\circ}[/tex]
[tex]\implies m\angle R=20^{\circ}[/tex]
Hence, the measure of angle R is 20°.
