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
△
A
B
C
∼
△
S
R
T
, what is m∠B
m
∠
B
?

Answer 1

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

In triangle \( SRT \):

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

To find the measure of angle \( B \) in triangle \( ABC \), we use the fact that the sum of angles in a triangle is \( 180^\circ \).

Since \( m\angle C = 34^\circ \) and \( m\angle A = 90^\circ \) in triangle \( ABC \):

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

Substituting the values we have:

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

Now, combine the known angles:

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

To isolate \( m\angle B \):

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

Therefore, the measure of angle \( B \) is:

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