In the figure, AB is parallel to CD. In triangle ABC, angle ABC = 65° and angle ACD = 38°. Find angle BAC.
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Worked Solution
Step 1: Identify the alternate interior angles.
AB ∥ CD and AC is a transversal.
Angle ACD = angle BCA = 38° (alternate interior angles).
Step 2: Apply the angle sum of a triangle.
Angle BAC + angle ABC + angle BCA = 180°
Angle BAC + 65° + 38° = 180°
Angle BAC + 103° = 180°
Angle BAC = 180° − 103°
Angle BAC = 77°
Correct answer: 77°
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