Question

d. x & 135°
n:
r:
x=

135° & y
n:
r:
y=

Explanation:

For \( x \) and \( 135^\circ \):

Step1: Identify angle relationship (supplementary)

\( x + 135^\circ = 180^\circ \) (linear pair, supplementary angles)

Step2: Solve for \( x \)

\( x = 180^\circ - 135^\circ \)
\( x = 45^\circ \)

For \( 135^\circ \) and \( y \):

Step1: Identify angle relationship (corresponding or alternate, parallel lines)

Assuming the lines are parallel, \( y = x \) (alternate interior angles or vertical angles, and \( x = 45^\circ \) from above)

Step2: Determine \( y \)

Since \( x = 45^\circ \), \( y = 45^\circ \) (or using supplementary with a right angle? Wait, from the diagram, the vertical line is straight, so \( 135^\circ \) and the angle adjacent to \( y \) (if we consider the transversal) – actually, since \( x = 45^\circ \), and \( y \) is equal to \( x \) because of parallel lines (alternate interior angles), so \( y = 45^\circ \). Alternatively, \( 135^\circ + 90^\circ + y = 360^\circ \)? No, better to use linear pair and vertical angles. Wait, the first part: \( x \) and \( 135^\circ \) are supplementary, so \( x = 45^\circ \). Then, \( y \) is equal to \( x \) because they are alternate interior angles (since the two slanted lines are parallel, as they have the same direction). So \( y = 45^\circ \).

Answer:

(for \( x \)): \( 45^\circ \)