Geometry Basics • Topic 5 of 5

Angle Relationships

When lines meet or cross, the angles they form follow fixed rules. Vertically opposite angles (across an intersection) are equal. Angles on a straight line form a linear pair and sum to 180°. Angles around a point sum to 360°. When two angles are in a given ratio and also complementary or supplementary, split the total (90° or 180°) into the ratio’s parts to find each. These relationships let you find many unknown angles from just one or two given values, a skill the SAT tests directly and as a step inside triangle and parallel-line problems. Look for intersecting lines and straight lines to apply them.

Two crossing lines showing equal vertical angles 70 and 110 degreesAngle relationships70°70°110°110°Vertical angles equal; a linear pair sums to 180°.

✅ Solved examples

1. Two lines cross; one angle is 70°. Find its vertical angle.
Vertical angles are equal: 70°.
2. Two angles form a straight line; one is 130°. Find the other.
180 − 130 = 50°.
3. Two supplementary angles are in ratio 2:3. Find the larger.
Parts: 180 ÷ 5 = 36; larger = 3 × 36 = 108°.
4. Three angles around a point are 120°, 150°, and x. Find x.
360 − 120 − 150 = 90°.

✏️ Practice — try these, take hints as needed

1. Two lines cross; one angle is 55°. Find its vertical angle.
Vertical angles are…
Equal.
—
55°.
2. Two angles on a straight line; one is 75°. Find the other.
They sum to 180°.
180 − 75.
—
105°.
3. Two complementary angles are in ratio 1:4. Find the larger.
90 ÷ 5 = 18 per part.
Larger = 4 parts.
—
72°.
4. Angles around a point: 100°, 130°, x. Find x.
They sum to 360°.
360 − 100 − 130.
—
130°.
5. Two supplementary angles in ratio 1:5. Find the smaller.
180 ÷ 6 = 30.
Smaller = 1 part.
—
30°.

📝 Topic test — 8 questions

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