SAT
Topic 1
Lines & angles
Angle pairs and parallel-line relationships.
Concept
The angle vocabulary you'll see again and again on the SAT:
- Complementary angles sum to 90°.
- Supplementary angles sum to 180° (a straight line).
- Vertical angles — formed by two intersecting lines, opposite each other. Always congruent (equal measure).
- Linear pair — two adjacent angles whose non-shared sides form a straight line. Always supplementary.
When two parallel lines are cut by a transversal:
- Corresponding angles — congruent.
- Alternate interior angles — congruent.
- Same-side (co-interior) angles — supplementary.
Worked example 1
Two lines intersect. One angle measures 65°. Find its vertical angle and its supplement.
Solution
Vertical. Vertical angles are congruent: vertical angle = 65°.
Supplement. Supplementary angles sum to 180°: 180 − 65 = 115°.
Vertical: 65°. Supplement: 115°.
Worked example 2
Lines ℓ ∥ m are cut by a transversal. One of the formed angles measures 70°. Find the corresponding angle and the alternate interior angle.
Solution
Corresponding. Parallel lines preserve corresponding angles ⇒ 70°.
Alternate interior. Also congruent for parallel lines ⇒ 70°.
Both are 70°. (The same-side interior angle would be 180 − 70 = 110°.)
Practice test
8 questions on supplements, complements, vertical angles, and parallel-line / transversal relationships.
Practice test · 8 questions
Question 1 of 8 · Score 0