Question

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△ abc ~△ efg
given m∠c = 52° and m∠e = 61°, what is m∠b?
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□°

Explanation:

Step1: Recall Similar Triangles Property

Similar triangles have corresponding angles equal. So, \( \angle A \) corresponds to \( \angle E \), so \( m\angle A = m\angle E = 61^\circ \).

Step2: Use Triangle Angle Sum

The sum of angles in a triangle is \( 180^\circ \). For \( \triangle ABC \), \( m\angle A + m\angle B + m\angle C = 180^\circ \). Substitute \( m\angle A = 61^\circ \) and \( m\angle C = 52^\circ \): \( 61 + m\angle B + 52 = 180 \).

Step3: Solve for \( m\angle B \)

Simplify the left side: \( 113 + m\angle B = 180 \). Subtract 113 from both sides: \( m\angle B = 180 - 113 = 67 \).

Answer:

\( 67 \)