Question

In the figure given below, find angle ABD. Also, find angle ABC, if angle C = 3 angle ABC.
​

Answer 1

Answer:

Angle ABD=30°

Angle ABC=20°

Step-by-step explanation:

Given: Angle ADB= 70°

Angle CAB= 100°

To find: Angle ABD

Angle ABC

Angle CAB+Angle DAB=180° (linear pair)

=> 100°+Angle DAB=180°

=> Angle DAB=80°

Let's consider ∆ABD

Angle ABD+Angle DCB+Angle ADB=180° (asp of a ∆)

=> Angle ABD+80°+70°=180°

=> Angle ABD=30°

Let Angle ABC be 'x°'

Then, Angle DCB will be '3x°'

Angle CBD = '30°+x°'

Let's consider ∆CBD

Angle CBD+Angle DAB+Angle CDB=180° (asp of a ∆)

=> 30°+x°+3x°+70°=180°

=> 4x°+100°=180°

=> 4x°=80°

=> x°=20°

Angle ABC=20°

hope it helps!