Question

In the diagram above, if ∠BOE is twice the ∠DOE, then find the value of ∠BOE.

• A. ${72}^{\circ }$
• B. ${64}^{\circ }$
• C. ${36}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is A ${72}^{\circ }$


$Given,\angle BOE=2\times \angle DOE$

$Let\angle DOE=x^{\circ }$
$\Rightarrow \angle BOE=2x^{\circ }$

$\angle AOC={108}^{\circ }$

$\angle AOC\text{and}\angle DOB\text{are vertical angles}$

We know, vertical angles are congruent.

$So,\angle AOC=\angle DOB={108}^{\circ }$

$Now,\angle DOB=\angle DOE+\angle BOE$

$So,\angle DOE+\angle BOE={108}^{\circ }$
$\Rightarrow x^{\circ }+2x^{\circ }={108}^{\circ }$
$\Rightarrow 3x^{\circ }={108}^{\circ }$
$\Rightarrow x^{\circ }=\frac{{108}^{\circ }}{3}={36}^{\circ }$

$\therefore \angle BOE=2x^{\circ }=2\times {36}^{\circ }={72}^{\circ }$