Question

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

Explanation:

Step1: Recall triangle angle sum and similarity

In similar triangles, corresponding angles are equal. Also, the sum of angles in a triangle is \(180^\circ\). For \(\triangle NKM\), angles are \(26^\circ\), \(105^\circ\), and \(\angle M\). For \(\triangle ABC\), \(\angle C = 26^\circ\), so \(\angle B\) corresponds to \(\angle K\), \(\angle C\) to \(\angle N\), and \(\angle A\) to \(\angle M\).

Step2: Find \(\angle M\) in \(\triangle NKM\)

Sum of angles in a triangle: \(26^\circ + 105^\circ + \angle M = 180^\circ\)
\(\angle M = 180^\circ - 26^\circ - 105^\circ = 49^\circ\)

Step3: Find \(\angle B\) in \(\triangle ABC\)

Since \(\triangle ABC \sim \triangle NKM\), \(\angle B = \angle K = 105^\circ\)

Step4: Find \(\angle A\) in \(\triangle ABC\)

Since \(\triangle ABC \sim \triangle NKM\), \(\angle A = \angle M = 49^\circ\) (or use angle sum: \(180^\circ - 105^\circ - 26^\circ = 49^\circ\))

Answer:

angle B = \(105^\circ\)
angle M = \(49^\circ\)
angle A = \(49^\circ\)