Geometry Basics • Topic 4 of 5

Angles

An angle is formed by two rays meeting at a vertex, measured in degrees from 0° to 360°. Angles are classified by size: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), and straight (exactly 180°). Two angles are complementary if they add to 90° and supplementary if they add to 180°, which lets you find an unknown angle by subtracting from 90 or 180. These ideas are everywhere on the SAT — in triangles, parallel-line diagrams and polygons. Knowing the classifications and the complementary/supplementary relationships lets you set up quick equations for missing angles.

Acute, right and obtuse angles comparedTypes of anglesAcuteRightObtuse

✅ Solved examples

1. Classify an angle measuring 47°.
Less than 90°, so acute.
2. Two angles are complementary; one is 30°. Find the other.
90 − 30 = 60°.
3. Classify an angle measuring 125°.
Between 90° and 180°, so obtuse.
4. Two angles are supplementary; one is 110°. Find the other.
180 − 110 = 70°.

✏️ Practice — try these, take hints as needed

1. Classify an angle measuring 90°.
Exactly 90°.
—
—
Right.
2. Two complementary angles; one is 25°. Find the other.
Sum is 90°.
90 − 25.
—
65°.
3. Classify an angle measuring 15°.
Below 90°.
—
—
Acute.
4. Two supplementary angles; one is 65°. Find the other.
Sum is 180°.
180 − 65.
—
115°.
5. Classify an angle measuring 180°.
A straight line.
—
—
Straight.

📝 Topic test — 8 questions

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