Triangle ABC is isosceles with AB = AC. Side AB is extended to a point D such that BD = BC. Given that ∠BCD = 32°, find ∠BAC.
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Worked Solution
Step 1: In triangle BDC, BD = BC so it is isosceles. The base angles are equal: angle BDC = angle BCD = 32°.
Step 2: Angle DBC = 180° − 32° − 32° = 116° (angle sum of triangle).
Step 3: Since AB is extended to D, angles ABC and DBC lie on a straight line: angle ABC = 180° − 116° = 64°.
Step 4: Triangle ABC is isosceles with AB = AC, so angle ACB = angle ABC = 64°.
Step 5: Angle BAC = 180° − 64° − 64° = 52°.
Answer: 52°
Correct answer: 52°
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