Choose a representation
Name the angle relationship before equating expressions. For an exterior triangle angle, add the two remote interior angles. Recover a length factor by taking the square root of an area factor.
Worked example
Two parallel lines are cut by a transversal. A pair of corresponding angles measures (3 x+4)° and (x+16)°. What is x? Corresponding angles are equal because the two lines are parallel. Set the expressions equal and solve after gathering x terms. Substitute the given numbers: (16-4) ÷ (3-1) = 6. The requested value is 6.
Contrast a wrong operation
In that example, 40 follows this error: Treat the corresponding angles as supplementary. The correct requested value is 6. Explain which quantity the mistaken method is actually calculating.
Connect a second form
An exterior angle of a triangle measures 84°. One remote interior angle measures 34°. What is the other remote interior angle? An exterior angle equals the sum of the two remote interior angles. Subtract the known remote angle, rather than the adjacent interior angle. Substitute the given numbers: 84-(34) = 50. The requested value is 50.
Transfer and check
Two parallel lines are cut by a transversal. A pair of corresponding angles measures (3 x+5)° and (x+19)°. What is x? Pause before checking. Answer: 7. Corresponding angles are equal because the two lines are parallel. Set the expressions equal and solve after gathering x terms. Substitute the given numbers: (19-5) ÷ (3-1) = 7.
Boundaries of the method
Vertical angles are equal, while a linear pair is supplementary. Corresponding angles require a parallel-line fact. Area ratios are not side-length ratios. This lesson samples a PSAT/NMSQT objective; its examples are original and do not claim official question status or full coverage.
Two parallel lines are cut by a transversal. A pair of corresponding angles measures (3 x+4)° and (x+16)°. What is x?
- Corresponding angles are equal because the two lines are parallel.
- Set the expressions equal and solve after gathering x terms.
- Substitute the given numbers: (16-4) ÷ (3-1) = 6.
- The requested value is 6.
Compare the other answer choices
Include the shared constant in the solution even though it cancels.
Stop after finding 2 x rather than x.
Treat the corresponding angles as supplementary.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Math specifications