Question

find the values of x and y.
(2x + 25)°
y°
(3x - 10)°
x =
y =

Explanation:

Step1: Identify Vertical Angles

The angles \( (2x + 25)^\circ \) and \( (3x - 10)^\circ \) are vertical angles, so they are equal.

$$ 2x + 25 = 3x - 10 $$

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides:

$$ 25 = x - 10 $$

Add 10 to both sides:

$$ x = 35 $$

Step3: Find \( y \)

The angle \( y^\circ \) and either \( (2x + 25)^\circ \) or \( (3x - 10)^\circ \) are supplementary (they form a linear pair, so their sum is \( 180^\circ \)). First, find \( 2x + 25 \) when \( x = 35 \):

$$ 2(35) + 25 = 70 + 25 = 95 $$

Then, \( y + 95 = 180 \), so:

$$ y = 180 - 95 = 85 $$

Answer:

\( x = 35 \), \( y = 85 \)