Question

In ∆ABC, ∠Α = 50°, ∠B = 70° and bisector of ∠C meets AB in D (see figure). Measure of ∠ADC is ______.

Options

• 50°

• 100°

• 30°

• 70°

Answer 1

In ∆ABC, ∠Α = 50°, ∠B = 70° and bisector of ∠C meets AB in D (see figure). Measure of ∠ADC is 100°.

Explanation:

In ∆ADC,

∠ADC + ∠DAC + ∠ACD = 180°  ...[Angle sum property of a triangle]

⇒ ∠ADC + 50° + ∠ACD = 180°  ...[∵ ∠DAC = 50°]

⇒ ∠ACD = 130° – ∠ADC  ...(i)

In ∆DBC,

∠ADC = ∠DBC + ∠BCD  ...[∵ Exterior angle is equal to the sum of opposite interior angles]

⇒ ∠ADC = 70° + ∠ACD  ...[∵ ∠ACD = ∠BCD]

⇒ ∠ADC = 70° + 130° – ∠ADC  ...[From equation (i)]

⇒ ∠ADC = 200° – ∠ADC

⇒ 2∠ADC = 200°

⇒ ∠ADC = `200^circ/2`

⇒ ∠ADC = 100°