Find the value of X. Then find the measure of each labeled angle.

The value of x is 15°.

Solution:

Given figure is a trapezoid.

Interior angles of the trapezoid are (2x + 65)° and (3x + 40)°.

Property of trapezoid:

Consecutive interior angles are supplementary.

⇒ (2x + 65)° + (3x + 40)° = 180°

⇒ 2x° + 65° + 3x° + 40° = 180°

Arrange like terms together.

⇒ 2x° + 3x° + 65°  + 40° = 180°

⇒ 5x° + 105° = 180°

Subtract 105° from both sides of the equation, we get

⇒ 5x° + 105° – 105° = 180° – 105°

⇒ 5x° = 75°

Divide by 5 on both sides of the equation, we get

⇒ x° = 15°

The value of x is 15°.