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°.