ABCD is a rectangle. E is a point on side BC. A line is drawn from A to E. Given that ∠BAE = 25°, find ∠AEC.
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Worked Solution
Step 1: Identify the right angle in the rectangle.
ABCD is a rectangle, so ∠ABE = 90° (E lies on side BC, and B is a corner).
Step 2: Apply the angle sum of triangle ABE.
∠BAE + ∠ABE + ∠AEB = 180°.
25° + 90° + ∠AEB = 180°, so ∠AEB = 65°.
Step 3: Use the straight line BC.
B, E and C lie on the same straight side, so ∠AEB and ∠AEC are angles on a straight line.
∠AEB + ∠AEC = 180°.
Step 4: Solve for ∠AEC.
∠AEC = 180° − 65° = 115°.
Answer: 115°
Correct answer: 115°
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