Question

what is the measure of angle z? 26° w y 121° z 85° 95° 121° 52°

Explanation:

Step1: Find angle w

Angle \( w \) and the \( 26^\circ \) angle are vertical angles? No, wait, they are alternate? Wait, actually, the \( 26^\circ \) angle and angle \( w \) are vertical angles? Wait, no, the \( 26^\circ \) angle and angle \( w \) are vertical angles? Wait, no, the horizontal line is intersected by a transversal, so the \( 26^\circ \) angle and angle \( w \) are vertical angles? Wait, no, actually, the \( 26^\circ \) angle and angle \( w \) are vertical angles? Wait, no, the \( 26^\circ \) angle and angle \( w \) are vertical angles, so \( w = 26^\circ \)? Wait, no, wait, the \( 26^\circ \) angle and angle \( w \) are vertical angles? Wait, no, the \( 26^\circ \) angle and angle \( w \) are vertical angles? Wait, no, the horizontal line is intersected by a transversal, so the \( 26^\circ \) angle and angle \( w \) are vertical angles, so \( w = 26^\circ \). Wait, no, actually, the \( 26^\circ \) angle and angle \( w \) are vertical angles, so \( w = 26^\circ \).

Step2: Find angle y

Angle \( y \) and the \( 121^\circ \) angle are supplementary because they form a linear pair. So \( y = 180^\circ - 121^\circ = 59^\circ \).

Step3: Find angle z

In a triangle, the sum of angles is \( 180^\circ \). Wait, the triangle has angles \( w \), \( y \), and the angle adjacent to \( z \)? Wait, no, angle \( z \) is vertical to the angle in the triangle. Wait, the triangle's angles are \( w = 26^\circ \), \( y = 59^\circ \), so the third angle in the triangle is \( 180^\circ - 26^\circ - 59^\circ = 95^\circ \). Then angle \( z \) is vertical to that angle, so \( z = 95^\circ \).

Answer:

\( 95^\circ \)