Question

5
.
AABC is isosceles with AB = AC, if ZA = 80°.
What is the measure of ZB?​

Answer 1

Question:

ΔABC is isosceles with AB = AC. If ∠A = 80°.  What is the measure of ∠B?​

Solution:

ATQ; AB = AC

Here, the angle opposite to AB is ∠ABC and the angle opposite to AC is ∠ABC. And, AB = AC.

We know that angles to opposite equal sides are also equal.

∴ ∠ABC = ∠ACB

According to ASP of a triangle;

⇒ ∠ABC + ∠BCA + ∠CAB = 180°

⇒ ∠n + ∠n + 80° = 180°

⇒ 2∠n = 180° - 80°

⇒ 2∠n = 100°

⇒ ∠n = 100°/2

⇒ ∠n = 50°

⇔ ∠ABC = ∠ACB = ∠n = 50°.

Therefore the measure of ∠B is 50°.