The value of x is 3.
Solution:
Given angles:
m∠D = 9x - 2, m∠C = 40° and ext∠B = 20x + 5
By exterior angle theorem of triangle,
The measure of exterior angle is equal to the sum of the two opposite interior angles.
⇒ ext∠B = m∠D + m∠C
⇒ 20x + 5 = 9x - 2 + 40
⇒ 20x + 5 = 9x + 38
Subtract 5 from both sides.
⇒ 20x = 9x + 33
Subtract 9x from both sides.
⇒ 11x = 33
Divide by 11 on both sides.
⇒ x = 3
The value of x is 3.