Question

3. Calculer la mesure des angles ADC et ABC de la figure ci-dessous.

Answer 1

< ADC = 113° . < ABC = 85°
Explanation:
the sum of the 3 angles in a triangle = 180°, then
- ADC + < ACD + < CAD = 180°, that is
- ADC + 39° + 28° = 180°
< ADC + 67° = 180° ( subtract 67° from both sides )
< ADC = 113°
DA is an angle bisector of < BAC, then
< BAD = < CAD = 28°, then < BAC = 56°, then
< ABC + < BAC + < ACB = 180°, that is
< ABC + 56° + 39° = 180°
< ABC + 95° = 180° ( subtract 95° from both sides )
< ABC = 85°

Answer 2

∠ ADC = 113° , ∠ ABC = 85°

Explanation:

the sum of the 3 angles in a triangle = 180° , then

∠ ADC + ∠ ACD + ∠ CAD = 180° , that is

∠ ADC + 39° + 28° = 180°

∠ ADC + 67° = 180° ( subtract 67° from both sides )

∠ ADC = 113°

---------------------------

DA is an angle bisector of ∠ BAC , then

∠ BAD = ∠ CAD = 28° , then ∠ BAC = 56° , then

∠ ABC + ∠ BAC + ∠ ACB = 180° , that is

∠ ABC + 56° + 39° = 180°

∠ ABC + 95° = 180° ( subtract 95° from both sides )

∠ ABC = 85°