Question

find the unknown angle measure in the pair of similar triangles. angle b = □° angle m = □° angle a = □° (simplify your answers. type an integer or a fraction.)

Explanation:

Step1: Recall angle - sum property of triangles

The sum of interior angles of a triangle is $180^{\circ}$. Also, for similar triangles, corresponding angles are equal.

Step2: Find angle $M$

Since the triangles are similar, $\angle M=\angle C = 11^{\circ}$ (corresponding angles of similar triangles).

Step3: Find angle $B$

In $\triangle NKM$, $\angle N = 11^{\circ}$ and $\angle K=101^{\circ}$. Using the angle - sum property of triangles ($\angle N+\angle K+\angle M = 180^{\circ}$), and since $\triangle ABC\sim\triangle NKM$, $\angle B=\angle K = 101^{\circ}$.

Step4: Find angle $A$

In $\triangle ABC$, we know $\angle B = 101^{\circ}$ and $\angle C=11^{\circ}$. Using the angle - sum property of triangles ($\angle A+\angle B+\angle C = 180^{\circ}$), we have $\angle A=180^{\circ}-\angle B - \angle C=180^{\circ}-101^{\circ}-11^{\circ}=68^{\circ}$.

Answer:

angle B = $101^{\circ}$
angle M = $11^{\circ}$
angle A = $68^{\circ}$