The interior angles of any triangle sum to 180° in measure, and in ∆ABC, the angles at vertices A and C are congruent. If we call their measure a, then
24° + 2a = 180° ⇒ 2a = 156° ⇒ a = 78°
The angle at vertex C and the angle with measure (2x - 18)° are supplementary, meaning they add up to 180° :
a + (2x - 18)° = 180°
Solve for x :
78° + (2x - 18)° = 180°
(2x - 18)° = 102°
2x = 120
x = 60
