Question

/_ABC is a straight angle. Find the value of x and then solve for the measure of /_ABD , /_EBC and /_CBA . Round to the nearest degree if necessary.

Answer 1

Given that ∠ABC is a straight angle:

∠ABD + ∠DBE + ∠EBC = 180°

6x + 5 + 92 + 2 + 3x = 180

(6x + 3x) + (5 + 92 + 2) = 180

9x + 99 = 180

9x = 180 - 99

9x = 81

x = 81/9

x = 9

m∠ABD = 6(9) + 5 = 59°

m∠EBC = 2 + 3(9) = 29°

m∠CBA = m∠ABC = 180°