In triangle ABC, AB = AC and angle BAC = 40°. D is a point outside the triangle such that BD = BC and angle DBC = 50°. Find angle BDC.
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Worked Solution
Step 1: Find the base angles of isosceles triangle ABC (AB = AC).
angle ABC = angle ACB = (180° − 40°) ÷ 2 = 140° ÷ 2 = 70°
Step 2: Focus on triangle BDC. BD = BC, so triangle BDC is also isosceles.
The apex angle of triangle BDC is angle DBC = 50°.
Step 3: Find the base angles of triangle BDC.
angle BDC = angle BCD = (180° − 50°) ÷ 2 = 130° ÷ 2 = 65°
Answer: 65°
Correct answer: 65°
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