Question

In a triangle ABC, angle B=80 degrees, angle C=20 degrees. A line is drawn to any point D on BC. Find the measure of angle BDA. ​

Answer 1

Measure of angle BDA is 60°

Solution:

• angle B=80° & angle C=20°

• angle A + angle B + angle C =180°

( Angle sum property of triangle)

• angle A +80+20 = 180°

• angle A = 80°

•Now, lets say that AD is such that it

is angle bisector of angle A

• angle BAD = 80/2=40°

•<BAD+ < B + <BDA =180°( Angle

sum property of triangle)

• 40+80 +<BDA = 180°

• <BDA = 60°

Answer 2

20° < ∠BDA <  100°

Step-by-step explanation:

In a triangle ABC, ∠B=80°, ∠C=20°

∠A + ∠B + ∠C = 180°

=> ∠A + 80° + 20° = 180°

=> ∠A = 80°

A line is drawn to any point D on BC

=> ∠BDA  = ∠DAC +  ∠C

=> ∠BDA  = ∠DAC  + 20°

∠DAC > 0 °

=> ∠BDA  > 20°

∠BDA  = ∠DAC  + 20°

∠DAC = ∠A -  ∠BAD

=> ∠DAC  = 80° - ∠BAD

∠BDA  =  80° - ∠BAD + 20°

=>  ∠BDA  =   100° - ∠BAD

∠BAD > 0°

=> ∠BDA <  100°

20° < ∠BDA <  100°

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