In Δ ABC, ∠ B = 45°, ∠ C = 55° and bisector of A and C meet at point D. Find ∠ ADB and ∠ ADC.

Given: ∠ B = 45°, ∠ C = 55°

To find: ∠ ADB and ∠ ADC

Explanation:

In Δ ABC,

By angle sum property:

∠A + ∠B + ∠C = 180°

⇒ ∠A + 45° + 55° = 180°

⇒ ∠A + 100° = 180°

⇒ ∠A = 80°

As AD is bisector of ∠A,

∴ ∠BAD = ∠CAD = 1/2 ∠A

⇒∠BAD = ∠CAD = 1/2 (80°)

⇒∠BAD = ∠CAD = 40°

In ΔADB, we have

∠BAD+∠ABD+∠ADB = 180°

⇒ 40°+45° +∠ADB = 180°

⇒ 85° +∠ADB = 180°

⇒ ∠ADB = 95°

Since ∠ADB and ∠ADC form a linear pair.

∴ ∠ADB + ∠ADC = 180°

⇒ 95°+ ∠ADC = 180°

⇒ ∠ADC = 85°

Hence ∠ ADB and ∠ ADC are 95° and 85°.