Use the image to answer the question.

Question

An illustration shows two right triangles with congruent corresponding angles. Triangle A B C is larger than triangle S R T. In triangle A B C, angle A measures 90 degrees, angle B does not have a measurement, and angle C measures 34 degrees. In triangle S R T, angle S measures 90 degrees, angle R measures 56 degrees, and angle T measures 34 degrees.

If △ABC∼△SRT
, what is m∠B
?

(1 point)
m∠B =

°

Answer 1

Since triangles \( \triangle ABC \) and \( \triangle SRT \) are similar (indicated by \( \triangle ABC \sim \triangle SRT \)), their corresponding angles are equal.

In \( \triangle SRT \):

• \( m\angle S = 90^\circ \)
• \( m\angle R = 56^\circ \)
• \( m\angle T = 34^\circ \)

In \( \triangle ABC \):

• \( m\angle A = 90^\circ \)
• \( m\angle B \) (unknown)
• \( m\angle C = 34^\circ \)

Since the angles must sum to \( 180^\circ \) for a triangle, we can find \( m\angle B \):

For \( \triangle ABC \):

\[ m\angle A + m\angle B + m\angle C = 180^\circ \]

Substituting the known values:

\[ 90^\circ + m\angle B + 34^\circ = 180^\circ \]

Combining the constant values:

\[ 124^\circ + m\angle B = 180^\circ \]

Solving for \( m\angle B \):

\[ m\angle B = 180^\circ - 124^\circ = 56^\circ \]

Thus, the measurement of \( m\angle B \) is:

\[ \boxed{56^\circ} \]