Question

In each diagram the line BD bisects angle ABC. Find the measure of angle ABC​

Answer 1

∠ ABC = 134°

Explanation:

Given tat CD bisects ∠ ABC then

∠ DBC = ∠ ABD , substitute values

x - 33 =
`(x)/(2)` + 17 ( multiply through by 2 to clear the fraction )

2x - 66 = x + 34 ( subtract x from both sides )

x - 66 = 34 ( add 66 to both sides )

x = 100

Thus

∠ DBC = ∠ ABD = x - 33 = 100 - 33 = 67°

Hence

∠ ABC = ∠ DBC + ∠ ABD = 67° + 67° = 134°