D is a point on side AB of a triangle ABC such that CD is the bisector of…
2024
D is a point on side AB of a triangle ABC such that CD is the bisector of angle ACB. If angle A = 50° and angle B = 70°, then angle ADC is equal to :
- A.
30°
- B.
50°
- C.
70°
- D.
100°
Show answer & explanation
Correct answer: D
The interior angles of any triangle always add up to 180°, and a bisector of an angle splits it into two exactly equal halves.
In triangle ABC, angle ACB = 180° - angle A - angle B = 180° - 50° - 70° = 60°.
CD bisects angle ACB, so angle ACD = 60° ÷ 2 = 30°.
Since D lies on side AB, angle DAC is the same as angle A, that is 50°.
In triangle ADC, applying the angle-sum property: angle ADC = 180° - angle DAC - angle ACD = 180° - 50° - 30° = 100°.
As a check, A, D and B lie on one straight line, so angle ADC and angle BDC together make 180°. In triangle BDC, angle BDC = 180° - angle B - angle BCD = 180° - 70° - 30° = 80°, giving angle ADC = 180° - 80° = 100°, the same result.
So angle ADC = 100°.