Question

In a angle ABC, AB = AC . if < B= 30° , what is the measure of < A​

Answer 1

Answer:

$EDC=15°$

In △ABC

AB=AC

∠B=∠C (isosceles triangle property) (1)

∠ADC=∠B+30 (Exterior angle property) (2)

Also, ∠AED=∠EDC+∠C (Exterior angle property)

∠AED=∠EDC+∠B (From 1)

Now, given, AD=AE

hence, ∠ADE=∠AED (Isosceles triangle property)

Thus, ∠ADE=∠EDC+∠B

∠ADE+∠EDC=2∠EDC+∠B

∠ADC=2∠+∠B

∠B+30=2∠EDC+∠B (From 2)

∠EDC=15°