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

in ABC AB is extended through D mltCBD 30 and AB BC What is the measure of angle a class=

Respuesta :

Answer:

15°

Step-by-step 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 = [tex]\frac{180-150}{2}[/tex] = [tex]\frac{30}{2}[/tex] = 15

That is ∠a = 15°

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