∆ABC is isosceles with AB = BC. If B is twice the measure of angle A, find the measure of all the angles of the triangle.
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Answer:
∠A=45° , ∠B=90° , ∠C=45°
Step-by-step explanation:
AB=BC
∠A=∠C [angles opposite to equal sides are equal in a Δ]
let ∠A=∠C=x -(i)
then,
∠B= 2∠A [Given]
∴∠B = 2x [from eq(i) ] [let this be eq(ii)]
∠A+∠B+∠C=180° [angle sum property of a Δ]
x + x + 2x =180°
4x = 180°
x = 180/4 = 45°
∴∠A=∠C=45°
∠B=2x = 2 × 45° [ from eq (ii) ]
∴∠B = 90°
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