Question

1. diagram: horizontal line, vertical line (right angle), slanted line intersecting both. angles labeled ( y^circ ), ( x^circ ), ( 72^circ ), ( z^circ ).

Explanation:

Step1: Find \( x \)

A straight line is \( 180^\circ \), so \( x + 72 = 180 \). Solving for \( x \), we get \( x = 180 - 72 = 108 \).

Step2: Find \( z \)

The right angle is \( 90^\circ \), so \( z + 72 = 90 \). Solving for \( z \), we get \( z = 90 - 72 = 18 \).

Step3: Find \( y \)

Since \( y \), the right angle, and \( z \) are on a straight line (or using vertical angles/linear pairs), \( y + 90 + z = 180 \). We know \( z = 18 \), so \( y + 90 + 18 = 180 \), \( y = 180 - 108 = 72 \). Or, since \( y \) and the \( 72^\circ \) angle are vertical angles (or alternate angles), \( y = 72 \).

Answer:

If we assume we need to find \( x \), \( y \), \( z \):

• \( x = 108^\circ \)
• \( y = 72^\circ \)
• \( z = 18^\circ \)

(If the question was to find a specific angle, adjust accordingly. For example, if finding \( x \), the answer is \( 108^\circ \); for \( y \), \( 72^\circ \); for \( z \), \( 18^\circ \).)