Geometry and TrigonometryMediumAlternate interior angles with expressions
Geometry and Trigonometry practice question
Two parallel lines are cut by a transversal. A pair of alternate interior angles measure (4x − 10)° and (2x + 30)°. What is the value of x?
Answer: 20
Alternate interior angles between parallel lines are equal: 4x − 10 = 2x + 30. Subtract 2x: 2x − 10 = 30, so 2x = 40 and x = 20. Each angle is 70°.
Common wrong answers
- If you answered 10
- 10 comes from 2x = 20 — the −10 was subtracted from 30 instead of added: 30 + 10 = 40.
- If you answered 70
- 70 is each angle's measure in degrees, not x.
- If you answered 26.67
- 26.67 (80/3) comes from setting the sum to 180. Alternate interior angles are EQUAL, not supplementary.
More Geometry and Trigonometry questions
- Medium
In a 45°-45°-90° right triangle, each leg has length 5. What is the length of the hypotenuse? - Medium
A cylinder has a radius of 3 and a height of 10. What is its volume? (Use V = πr²h.) - Medium
In a right triangle, the side opposite angle θ has length 3 and the hypotenuse has length 5. What is sin θ? - Medium
Two triangles are similar with a ratio of 2 to 3. A side of the smaller triangle measures 8. What is the lengt… - Medium
What is the distance between the points (1, 2) and (4, 6) in the coordinate plane? - Medium
A circle has a radius of 6. What is the area of a sector with a central angle of 60°?
Not affiliated with the College Board. SAT is a trademark of the College Board.