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.

Question

if abc = srt, what is m∠b

Answer 1

In triangle \( ABC \), we know that angle \( A \) is \( 90^\circ \) and angle \( C \) is \( 34^\circ \). To find angle \( B \), we can use the fact that the angles in a triangle sum up to \( 180^\circ \).

So, we can find \( m \angle B \) using the equation:

\[ m \angle A + m \angle B + m \angle C = 180^\circ \] Substituting the known values:

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

Combining the known angles:

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

Now, subtract \( 124^\circ \) from both sides:

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

Thus, the measure of angle \( B \) in triangle \( ABC \) is:

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