Question

In the given figure, AB = BC and AC = CD. Find the ratio of ∠BAD: ∠ADB.

• A. 1: 3
• B. 3 : 2
• C. 3 :1
• D. 2:3

Answer 1

The correct option is C

3 :1

Let $\angle ADB$ = x

In ∆ACD, AC = CD

$\angle$CAD = $\angle$CDA = x

And ext. $\angle$ACB = $\angle$CAD + $\angle$CDA

In ABC, AB = BC

$\angle$BAC = $\angle$ACB = 2x

$\angle$BAD = $\angle$BAC + $\angle$CAD

= 2x + x

= 3x

And, $\frac{\angle BAD}{\angle ADB}$ = $\frac{3x}{x}$

$\angle$BAD: $\angle$ADB = 3: 1