In ΔABC, if m∠A=30° and mAB=mAC, then values of ∠B and ∠C are:
Question
In ΔABC, if m∠A=30° and mAB=mAC, then values of ∠B and ∠C are:
Solution
In a triangle, the sum of all angles is 180°.
Given that ΔABC is an isosceles triangle (since AB = AC), the base angles of an isosceles triangle are equal. This means ∠B = ∠C.
We know that ∠A = 30°.
So, ∠B + ∠C = 180° - ∠A = 180° - 30° = 150°.
Since ∠B = ∠C, we can say that 2∠B = 150°.
Therefore, ∠B = ∠C = 150° / 2 = 75°.
So, the values of ∠B and ∠C are 75° each.
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