Question

In the figure given, what are the values of b, c, and a respectively?

• A. ${18}^{\circ },{70}^{\circ },and{92}^{\circ }$
• B. ${92}^{\circ },{70}^{\circ },and{18}^{\circ }$
• C. ${70}^{\circ },{92}^{\circ },and{18}^{\circ }$
• D. ${70}^{\circ },{18}^{\circ },and{92}^{\circ }$

Answer 1

The correct option is C

${70}^{\circ },{92}^{\circ },and{18}^{\circ }$

Given: AB = BD
$\Rightarrow △BDA$ is an isosceles triangle as two sides are equal.
$\Rightarrow \angle BAD=\angle BDA={35}^{\circ }$
Using exterior angle property,
$\angle b=\angle BDA+\angle BAD$
$\Rightarrow \angle b={35}^{\circ }+{35}^{\circ }={70}^{\circ }$
Also given AC = CE
$\Rightarrow △CAE$ is an isosceles triangle as two sides are equal.
$\Rightarrow \angle CEA=\angle CAE={46}^{\circ }$
Using exterior angle property,
$\Rightarrow \angle c=\angle CAE+\angle CEA={46}^{\circ }+{46}^{\circ }={92}^{\circ }In\Delta ABC,\angle a+\angle b+\angle c={180}^{\circ }\Rightarrow \angle a={180}^{\circ }-\angle b-\angle c\Rightarrow \angle a={180}^{\circ }-{70}^{\circ }-{92}^{\circ }={18}^{\circ }\therefore \angle a={18}^{\circ },\angle b={70}^{\circ },and\angle c={92}^{\circ }$