Question

1. in the figure below, ( h parallel o ). find the values of ( x ) and ( y ).

Explanation:

Step1: Find x using corresponding angles

Since \( h \parallel o \), the \( 77^\circ \) angle and \( (3x - 28)^\circ \) are corresponding angles, so they are equal.
\[
3x - 28 = 77
\]
Add 28 to both sides:
\[
3x = 77 + 28 = 105
\]
Divide by 3:
\[
x = \frac{105}{3} = 35
\]

Step2: Find y using supplementary angles

The angle \( y^\circ \) and \( (3x - 28)^\circ \) are supplementary (they form a linear pair), so their sum is \( 180^\circ \). We know \( 3x - 28 = 77 \), so:
\[
y + 77 = 180
\]
Subtract 77 from both sides:
\[
y = 180 - 77 = 103
\]

Answer:

\( x = 35 \)
\( y = 103 \)