Given a right triangle where $m\angle x=34°$ and $m\angle z=26°$, what is the measure of the right angle in the triangle?

• A. $90°$
• B. $120°$
• C. $60°$
• D. $80°$

Answer: (A)

Verified step by step guidance

1. Recall that the sum of the interior angles in any triangle is always \(180^\circ\).
2. Since the triangle is a right triangle, one of its angles measures \(90^\circ\) by definition.
3. Given the measures of two other angles, \(m\angle x = 34^\circ\) and \(m\angle z = 26^\circ\), add these two angles together: \(34^\circ + 26^\circ\).
4. Subtract the sum of the two given angles from \(180^\circ\) to find the measure of the third angle: \(180^\circ - (34^\circ + 26^\circ)\).
5. Recognize that the third angle must be the right angle, which should measure \(90^\circ\), confirming the property of a right triangle.