Given a right triangle where the measure of angle $\angle 6$ is $32°$, what is the sum $m\angle 4+m\angle 5$ in degrees?

• A. $58°$
• B. $148°$
• C. $158°$
• D. $90°$

Answer: (C)

Verified step by step guidance

1. Recall that the sum of the interior angles in any triangle is always 180 degrees.
2. Since the triangle is a right triangle, one of its angles is 90 degrees.
3. Given that angle \( \angle 6 = 32^\circ \), use the angle sum property to find the sum of the other two angles \( \angle 4 \) and \( \angle 5 \).
4. Set up the equation: \( \angle 4 + \angle 5 + \angle 6 + 90^\circ = 180^\circ \).
5. Solve for \( \angle 4 + \angle 5 \) by subtracting \( 32^\circ \) and \( 90^\circ \) from 180 degrees: \( \angle 4 + \angle 5 = 180^\circ - 90^\circ - 32^\circ \).