Geometry and TrigonometryEasy–MediumSame-side interior angles with a transversal
Geometry and Trigonometry practice question
Lines l and m are parallel and are cut by a transversal. Two same-side interior angles formed measure (3x + 10)° and (2x − 5)°. What is the value of x?
Answer: 35
Same-side interior angles between parallel lines are supplementary: (3x + 10) + (2x − 5) = 180, so 5x + 5 = 180, 5x = 175, x = 35. Check: 115° + 65° = 180°.
Common wrong answers
- If you answered 17
- 17 sets the sum to 90, treating the angles as complementary. Same-side interior angles add to 180.
- If you answered 37
- 37 comes from 5x = 185 — the −5 was added instead of subtracted. (3x + 10) + (2x − 5) = 5x + 5.
- If you answered -15
- −15 sets the two angles EQUAL, as if they were alternate interior or corresponding angles. Same-side interior angles are supplementary, not equal.
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