in triangle abc , angle b = 45 degree angle c = 55 degree and bisector af angle a meet bc at point d find the measure of angle adb and angle adc
plx help
Given: In ΔABC
∠B = 45°, ∠C = 55°
Now,
∠A + ∠B + ∠C = 180° (Angle sum property)
⇒ ∠A + 45° + 55° = 180°
⇒ ∠A = 180° – 100° = 80°
Also, AD is bisector of ∠A.
Now,
∠BAD + ∠ABD + ∠ADB = 180°
⇒ 40° + 45° + ∠ADB = 180°
⇒ ∠ADB = 180° – 85° = 95°
and ∠ADB + ∠ADC = 180°
⇒ ∠ADC = 180° – ∠ADB
= 180° – 95°
= 85°