Geometry and TrigonometryMediumExterior angle equals the two remote interior angles
Geometry and Trigonometry practice question
In triangle ABC, angle A measures 40°, and the exterior angle at vertex C measures 115°. What is the measure, in degrees, of angle B?
Answer: 75
An exterior angle equals the sum of the two interior angles not adjacent to it: 115 = 40 + B, so B = 75. (Equivalently, angle C = 65 and B = 180 − 40 − 65.)
Common wrong answers
- If you answered 25
- 25 is 65 − 40, subtracting from the interior angle at C instead of using the exterior angle.
- If you answered 65
- 65 is the INTERIOR angle at C (180 − 115), not angle B.
- If you answered 155
- 155 adds 115 and 40; the exterior angle is the SUM of A and B, so B = 115 − 40.
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