Geometry and TrigonometryVery hardExterior angle with two expressions
Geometry and Trigonometry practice question
In a triangle, two of the interior angles measure (x + 10)° and (2x − 5)°. The exterior angle at the third vertex measures 125°. What is the value of x?
Answer: 40
An exterior angle equals the sum of the two remote interior angles: (x + 10) + (2x − 5) = 125, so 3x + 5 = 125, 3x = 120, x = 40. (The angles are 50° and 75°; the third interior angle is 55°, whose exterior angle is 125°.)
Common wrong answers
- If you answered 35
- 35 comes from 3x + 5 = 110 or a similar slip in the constant; (x + 10) + (2x − 5) = 3x + 5.
- If you answered 45
- 45 comes from 3x − 5 = 125 with the +10 and −5 mishandled.
- If you answered 58.33
- 58.33 comes from 3x + 5 = 180, treating the exterior angle as the interior angle sum; the exterior angle equals the sum of the two REMOTE interior angles.
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