Skills · Geometry · Tools of Geometry

Angle addition and bisectors

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. angle ABC, ray BD inside it: ∠ABD 70°, ∠DBC ?, ∠ABC 135°BADC70°
    m∠ABC = 135°. Find m∠DBC.
  2. angle ABC, ray BD inside it: ∠ABD 96°, ∠DBC ?, ∠ABC 164°BADC96°
    m∠ABC = 164°. Find m∠DBC.
  3. angle ABC, bisected by ray BD: ∠DBC ?, ∠ABC 124°BADC
    Ray BD bisects ∠ABC. m∠ABC = 124°. Find m∠DBC.
  4. angle ABC, bisected by ray BD: ∠DBC 72°, ∠ABC ?BADC72°
    Ray BD bisects ∠ABC. Find m∠ABC.
  5. angle ABC, ray BD inside it: ∠ABD ?, ∠DBC 70°, ∠ABC 111°BADC70°
    m∠ABC = 111°. Find m∠ABD.
  6. angle ABC, bisected by ray BD: ∠ABD ?, ∠ABC 66°BADC
    Ray BD bisects ∠ABC. m∠ABC = 66°. Find m∠ABD.
  7. angle ABC, ray BD inside it: ∠ABD 26°, ∠DBC ?, ∠ABC 53°BADC26°
    m∠ABC = 53°. Find m∠DBC.
  8. angle ABC, bisected by ray BD: ∠DBC 64°, ∠ABC ?BADC64°
    Ray BD bisects ∠ABC. Find m∠ABC.

Answer key

  1. 65°
  2. 68°
  3. 62°
  4. 144°
  5. 41°
  6. 33°
  7. 27°
  8. 128°

Sample Sheet · Level 3

  1. angle ABC, ray BD inside it: ∠ABD (6x − 8)°, ∠DBC (5x + 2)°, ∠ABC 82°BADC(6x − 8)°(5x + 2)°
    m∠ABC = 82°. Find m∠DBC.
  2. angle ABC, ray BD inside it: ∠ABD (2x + 16)°, ∠DBC (x + 15)°, ∠ABC 118°BADC(2x + 16)°(x + 15)°
    m∠ABC = 118°. Find m∠ABD.
  3. angle ABC, bisected by ray BD: ∠ABD (x + 26)°, ∠DBC (2x + 6)°BADC(x + 26)°(2x + 6)°
    Ray BD bisects ∠ABC. Find m∠ABD.
  4. angle ABC, ray BD inside it: ∠ABD (9x + 37)°, ∠DBC (2x + 39)°, ∠ABC 98°BADC(9x + 37)°(2x + 39)°
    m∠ABC = 98°. Find m∠DBC.
  5. angle ABC, ray BD inside it: ∠ABD (3x + 37)°, ∠DBC (6x + 22)°, ∠ABC 122°BADC(3x + 37)°(6x + 22)°
    m∠ABC = 122°. Find m∠ABD.
  6. angle ABC, bisected by ray BD: ∠ABD (2x + 35)°, ∠DBC (3x + 10)°BADC(2x + 35)°(3x + 10)°
    Ray BD bisects ∠ABC. Find m∠ABD.
  7. angle ABC, bisected by ray BD: ∠ABD (2x + 14)°, ∠ABC (6x − 28)°BADC(2x + 14)°
    Ray BD bisects ∠ABC. m∠ABC = (6x − 28)°. Find m∠ABC.
  8. angle ABC, bisected by ray BD: ∠DBC (4x + 18)°, ∠ABC (9x + 27)°BADC(4x + 18)°
    Ray BD bisects ∠ABC. m∠ABC = (9x + 27)°. Find m∠DBC.

Answer key

  1. 42°
  2. 74°
  3. 46°
  4. 43°
  5. 58°
  6. 85°
  7. 140°
  8. 54°

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