Geometry and TrigonometryEasy–MediumVertical angles with expressions
Geometry and Trigonometry practice question
Two straight lines intersect at a point. A pair of vertical angles formed by the lines measure (2x + 10)° and (3x − 20)°. What is the value of x?
Answer: 30
Vertical angles are equal: 2x + 10 = 3x − 20. Subtract 2x: 10 = x − 20, so x = 30. Both angles then measure 70°.
Common wrong answers
- If you answered 10
- 10 is the constant in the first expression, not the solution. Solve 2x + 10 = 3x − 20.
- If you answered 38
- 38 comes from setting the sum to 180 (5x − 10 = 180). Vertical angles are EQUAL, not supplementary.
- If you answered 70
- 70 is the measure of each angle in degrees, not the value of x.
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