31,109 views
29 votes
29 votes
Find the value of x. Please help me with this?

Find the value of x. Please help me with this?-example-1
User WarHog
by
2.8k points

1 Answer

22 votes
22 votes

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

User Pedrom
by
2.4k points