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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 =

°
Remaining Attempts : 3
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Answer 1

In triangles \( ABC \) and \( SRT \), we are given that \( \triangle ABC \sim \triangle SRT \). Since the triangles are similar, their corresponding angles are equal.

Given the angles:

• In triangle \( ABC \):

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

• In triangle \( SRT \):

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

Since \( m\angle C = m\angle T \) and both are \( 34^\circ \), we have:

• \( m\angle B + m\angle R + m\angle A = 180^\circ \)

Using the angles in triangle \( SRT \): \[ m\angle R + m\angle T + m\angle S = 180^\circ \] \[ 56^\circ + 34^\circ + 90^\circ = 180^\circ \]

Now using triangle \( ABC \): Since \( m\angle A = 90^\circ \): \[ m\angle B + 34^\circ + 90^\circ = 180^\circ \]

We can simplify this: \[ m\angle B + 124^\circ = 180^\circ \]

Thus, solving for \( m\angle B \): \[ m\angle B = 180^\circ - 124^\circ \] \[ m\angle B = 56^\circ \]

So, the measure of angle \( B \) is: \[ m\angle B = 56^\circ \]