Question

An equilateral triangle and an isosceles triangle share a common side. What is the measure of ZABC? Please show your work and explain why B A 61° D​

Answer 1

∠ ABC = 118°

Explanation:

Δ BCD has 3 congruent (equal) sides and is equilateral

the 3 angles in an equilateral triangle are congruent , all 60°

Then ∠ CBD = 60°

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Δ ABD has 2 congruent sides and is isosceles

the base angles of an isosceles triangle are congruent , then

∠ BAD = ∠ BDA = 61°

The sum of the 3 angles in a triangle = 180° , then

∠ ABD + ∠ BAD + ∠ BDA = 180° ( substitute values )

∠ ABD + 61° + 61° = 180°

∠ ABD + 122° = 180° ( subtract 122° from both sides )

∠ ABD = 58°

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∠ ABC = ∠ ABD + ∠ CBD = 58° + 60° = 118°