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:

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