Question

Consider the triangles $△BCD$ and $△ACD:$

Find the exterior angle $\angle E.$

• A. ${145}^o$
• B. ${150}^o$
• C. ${155}^o$
• D. Insufficient data.

Answer 1

The correct option is C ${155}^o$

For the given figure,

the interior angle $\angle BCA={180}^o-{50}^o={130}^o.$
Also, the angle $\angle CDB={180}^o-{155}^o={25}^o$

For $△BCD,$
$\angle B={180}^o-\angle BCA-\angle CDB$
$\Rightarrow \angle B={180}^o-{130}^o-{25}^o={25}^o$

Arc CD subtends angle $\angle CBD$ at B and $\angle CAD$ at A on the same segment of the circle.

We know that the measure of all angles subtended by an arc on the same segment of the circle are equal.

$\therefore \angle CBD=\angle CAD={25}^o$

Hence, exterior angle $\angle E={180}^o-{25}^o={155}^o$