Question

if wx = wz = 26, m∠wyx = t + 26°, and m∠wyz = 3t, what is m∠xyz?

Explanation:

Step1: Identify Angle Bisector

Since \( WX = WZ = 26 \) and \( \angle WXY \) and \( \angle WZY \) are right angles, \( WY \) bisects \( \angle XYZ \). So \( m\angle WYX = m\angle WYZ \).

Step2: Solve for \( t \)

Set \( t + 26^\circ = 3t \).
Subtract \( t \) from both sides: \( 26^\circ = 2t \).
Divide by 2: \( t = 13^\circ \).

Step3: Find \( m\angle WYZ \)

Substitute \( t = 13^\circ \) into \( m\angle WYZ = 3t \): \( m\angle WYZ = 3\times13^\circ = 39^\circ \).

Step4: Find \( m\angle XYZ \)

Since \( WY \) bisects \( \angle XYZ \), \( m\angle XYZ = 2\times m\angle WYZ \).
So \( m\angle XYZ = 2\times39^\circ = 78^\circ \).

Answer:

\( 78 \)