In parallelogram ABCD, angle BAD = 64°. AB is extended to a point E such that CE = CB. Find angle BCE.
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Worked Solution
Step 1: In a parallelogram, consecutive angles are supplementary, so angle ABC = 180° − 64° = 116°.
Step 2: AB is extended to E, so angle CBE forms a linear pair with angle ABC: angle CBE = 180° − 116° = 64°.
Step 3: Triangle BCE is isosceles (CE = CB), so the two base angles are equal: angle BEC = angle CBE = 64°.
Step 4: Angles in triangle BCE add up to 180°, so angle BCE = 180° − 64° − 64° = 52°.
Answer: 52°
Correct answer: 52°
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