Question

given ( m parallel n ), find the value of ( x ) and ( y ).

Explanation:

Step1: Find x using alternate interior angles

Since \( m \parallel n \), the alternate interior angles \( (3x - 20)^\circ \) and \( (2x + 3)^\circ \) are equal.

$$ 3x - 20 = 2x + 3 $$

Subtract \( 2x \) from both sides:

$$ x - 20 = 3 $$

Add 20 to both sides:

$$ x = 23 $$

Step2: Find y using linear pair

The angles \( (3x - 20)^\circ \) and \( (y - 6)^\circ \) form a linear pair, so their sum is \( 180^\circ \). First, substitute \( x = 23 \) into \( 3x - 20 \):

$$ 3(23) - 20 = 69 - 20 = 49 $$

Now, set up the equation for the linear pair:

$$ 49 + (y - 6) = 180 $$

Simplify the left side:

$$ 43 + y = 180 $$

Subtract 43 from both sides:

$$ y = 137 $$

Answer:

\( x = 23 \), \( y = 137 \)