Question

given m || n, find the value of x and y. y° (4x+6)° m (5x-1)° n answer attempt 1 out of 2 x = y =

Explanation:

Step1: Identify Alternate Interior Angles

Since \( m \parallel n \), the angles \( (5x - 1)^\circ \) and \( (4x + 6)^\circ \) are alternate interior angles, so they are equal.

$$ 5x - 1 = 4x + 6 $$

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides:

$$ 5x - 4x - 1 = 4x - 4x + 6 $$

$$ x - 1 = 6 $$

Add 1 to both sides:

$$ x - 1 + 1 = 6 + 1 $$

$$ x = 7 $$

Step3: Find \( (4x + 6)^\circ \)

Substitute \( x = 7 \) into \( 4x + 6 \):

$$ 4(7) + 6 = 28 + 6 = 34 $$

Step4: Find \( y \)

The angle \( y^\circ \) and \( (4x + 6)^\circ \) are supplementary (linear pair), so:

$$ y + 34 = 180 $$

Subtract 34 from both sides:

$$ y = 180 - 34 = 146 $$

Answer:

\( x = 7 \), \( y = 146 \)