Question

In the given figure $AB=AC$, $BC=CD$ and $DE||BC$. Find the measure of $x$.

• A. $54$
• B. $61$
• C. $58$
• D. $72$

Answer 1

The correct option is C $58$

Angle PFE is exterior angle of triangle ABC.and AB=AC,
So, $\angle ABC=\angle ACB$
And we know that An measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
So, $\angle ABC+\angle ACB=122$
$\angle ABC+\angle ABC=122$
$\angle ABC=61$
And $DE||BC$ , so $\angle ABC+\angle BDE=180$
$61+\angle BDE=180$
$\angle BDE=119$
as BC=CD , So, $\angle BDC=\angle ABC=61$
$\angle BDE=\angle BDC+x=119$
$x+61=119$
$x=58$
Answer (C) 58