Tayarri SAT
Math, Geometry and Trigonometry, Stage 3

Lines, angles and triangles on the SAT

Angles in a triangle add to 180°, angles on a straight line add to 180°, and angles around a point add to 360°. With parallel lines, corresponding and alternate angles are equal, and same-side interior angles add to 180°. Similar triangles have equal angles and proportional sides.

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RuleExample
Triangle sum 180°70° + 43° + 67°
Exterior angle = sum of two opposite interior angles47° + 33° = 80°
Isosceles: base angles equalapex 92° → 44° each
Polygon interior sum (n − 2) × 180°hexagon: 720°

Similar triangles

Find the scale factor from one pair of matching sides, then multiply. PQ = 8 matches ST = 32 (factor 4), so QR = 7 matches TU = 28.

Common mistakes

Using 360° for a triangleTriangles total 180°.
Parallel-line pairsOnly two angle sizes appear: x and 180° − x.
Adding instead of scalingSimilar sides multiply by the scale factor.

Sample questions with answers

1. Angles A = 70° and B = 43°. Angle C?
  1. 113°
  2. 67° (correct)
  3. 247°
  4. 74°

180 − 70 − 43 = 67.

2. Parallel lines; one angle is 52°. Alternate interior angle?
  1. 128°
  2. 38°
  3. 52° (correct)
  4. 308°

Alternate interior angles are equal.

3. Each interior angle of a regular hexagon?
  1. 108°
  2. 120° (correct)
  3. 135°
  4. 720°

720 ÷ 6 = 120.

Frequently asked questions

What angle rules does the SAT test?

Triangle sums, parallel lines, exterior angles, isosceles triangles, polygons and similarity. Geometry and Trigonometry makes up about 15% of SAT Math, roughly 5 to 7 questions. A reference sheet with key formulas is available during the test.

How do I use similar triangles?

Find the ratio between matching sides, then multiply the other sides by it.

What is the exterior angle theorem?

An exterior angle equals the sum of the two opposite interior angles.

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