Skills · Geometry · Triangles

Triangle angle sum and exterior angles

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

Sample Sheet · Level 1

  1. triangle ABC, side AB carried on to D: remote interior angles ∠A 62° and ∠C 54°, exterior angle ∠CBD ?ABCD62°54°?
    Find the measure of the angle marked ?.
  2. right triangle ABC, the right angle at C: ∠A 48°, ∠B ?ABC48°?
    Find the measure of the angle marked ?.
  3. triangle ABC, side AB carried on to D: remote interior angles ∠A 96° and ∠C 52°, exterior angle ∠CBD ?ABCD96°52°?
    Find the measure of the angle marked ?.
  4. right triangle ABC, the right angle at A: ∠B 26°, ∠C ?ABC26°?
    Find the measure of the angle marked ?.
  5. triangle ABC, side AB carried on to D: remote interior angles ∠A 31° and ∠C 66°, exterior angle ∠CBD ?ABCD31°66°?
    Find the measure of the angle marked ?.
  6. triangle ABC: ∠A ?, ∠B 36°, ∠C 95°ABC?36°95°
    Find the measure of the angle marked ?.
  7. right triangle ABC, the right angle at C: ∠A 33°, ∠B ?ABC33°?
    Find the measure of the angle marked ?.
  8. triangle ABC: ∠A ?, ∠B 82°, ∠C 69°ABC?82°69°
    Find the measure of the angle marked ?.

Answer key

  1. 116°
  2. 42°
  3. 148°
  4. 64°
  5. 97°
  6. 49°
  7. 57°
  8. 29°

Sample Sheet · Level 3

  1. triangle ABC: ∠A (x + 15)°, ∠B (4x − 24)°, ∠C 39°ABC(x + 15)°(4x − 24)°39°
    Find m∠A.
  2. right triangle ABC, the right angle at C: ∠A (2x + 12)°, ∠B (3x − 2)°ABC(2x + 12)°(3x − 2)°
    Find m∠B.
  3. triangle ABC, side AB carried on to D: remote interior angles ∠A (4x − 32)° and ∠C 89°, exterior angle ∠CBD (6x + 15)°ABCD(4x − 32)°89°(6x + 15)°
    Find m∠CBD.
  4. right triangle ABC, the right angle at C: ∠A (4x − 39)°, ∠B (2x + 9)°ABC(4x − 39)°(2x + 9)°
    Find m∠B.
  5. triangle ABC: ∠A (x + 27)°, ∠B (2x − 14)°, ∠C 83°ABC(x + 27)°(2x − 14)°83°
    Find m∠B.
  6. triangle ABC, side AB carried on to D: remote interior angles ∠A (3x − 9)° and ∠C (3x + 15)°, exterior angle ∠CBD 138°ABCD(3x − 9)°(3x + 15)°138°
    Find m∠A.
  7. The angles of a triangle are in the ratio 2 : 3 : 10. Find the smallest angle.
  8. The angles of a triangle are in the ratio 3 : 4 : 13. Find the smallest angle.

Answer key

  1. 45°
  2. 46°
  3. 141°
  4. 49°
  5. 42°
  6. 57°
  7. 24°
  8. 27°

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