In the figure, triangle ABC has AB = AC. Point D is on side BC such that AD = BD. Given that ∠ABD = 35°, find ∠DAC.
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Worked Solution
Step 1: Triangle ABD is isosceles (AD = BD), so its base angles are equal: angle BAD = angle ABD = 35°.
Step 2: Triangle ABC is also isosceles (AB = AC), so its base angles are equal: angle ABC = angle ACB. Since D is on BC, angle ABC = angle ABD = 35°.
Step 3: Apex angle BAC = 180° − 35° − 35° = 110°.
Step 4: Angle DAC = angle BAC − angle BAD = 110° − 35° = 75°.
Answer: 75°
Correct answer: 75°
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