Question

In ∆ABC, AB is extended through D, m<CBD =30 and AB = BC. What is the measure of angle a​

Answer 1

15°

Explanation:

∠ABC and ∠DBC form a straight angle and are supplementary, thus

∠ABC + 30 = 180 ( subtract 30 from both sides )

∠ABC = 150°

Since AB = BC then ΔABC is isosceles with ∠BAC = ∠BCA

The sum of the 3 angles in the triangle = 180°

Hence ∠BAC =
`(180-150)/(2)` =
`(30)/(2)` = 15

That is ∠a = 15°