Geometry and TrigonometryMediumExterior angle at the base of an isosceles triangle
Geometry and Trigonometry practice question
In triangle ABC, AB = AC and angle A measures 100°. Side CB is extended past B to point D. What is the measure, in degrees, of angle ABD?
Answer: 140
Since AB = AC, the base angles at B and C are equal: (180 − 100)/2 = 40° each. Angle ABD is the exterior angle at B, supplementary to the 40° interior angle: 180 − 40 = 140°. (Equivalently, it equals the sum of the two remote interior angles: 100 + 40.)
Common wrong answers
- If you answered 40
- 40 is the INTERIOR angle at B. Angle ABD is the exterior angle, which makes a straight line with it: 180 − 40.
- If you answered 80
- 80 is 180 − 100, the two base angles together. Each base angle is 40°, and the exterior angle is 140°.
- If you answered 100
- 100 is angle A. The exterior angle at B equals angle A plus angle C: 100 + 40 = 140.
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