Question

In the given figure, AC = AD = CD = BD. Then the measure of angle ABC is

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B

${30}^{\circ }$

Given, AC = AD = CD.

Then triangle ACD is an equilateral triangle.

Then $\angle CAD=\angle ADC=\angle DCA={60}^{\circ }$ [In any equilateral triangle, all angles are ${60}^{\circ }$]

Now, $\angle CDA=\angle DAB+\angle DBA$ (Since exterior angle is the sum of opposite interior angles)

But $\angle DAB=\angle DBA$ (Since AD = DB)

$\therefore \angle DBA+\angle DBA=\angle CDA$

$2\angle DBA={60}^{\circ }$

$\angle DBA={30}^{\circ }$