Question

calculate the value of y.

y = 45
y = 77
y = 81
none of these

Explanation:

Step1: Find the value of \( x \)

Use the property that the sum of adjacent angles on a straight line is \( 180^{\circ} \). So, \( x + 77=180 \), then \( x = 180 - 77=103 \).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \( 180^{\circ} \). So, \( x + y+32 = 180 \). Substitute \( x = 103 \) into the equation: \( 103 + y+32 = 180 \).

Step3: Solve for \( y \)

Simplify the left - hand side of the equation: \( y+135 = 180 \). Then \( y=180 - 135 = 45 \).

Answer:

\( y = 45 \)