Question

In the given figure, AB || DE. ∠A = 43⁰ and ∠BDE = 57⁰. The value of ∠x is ________.

• A. 43${}^{\circ }$
• B. 57${}^{\circ }$
• C. 34${}^{\circ }$
• D. 75${}^{\circ }$

Answer 1

The correct option is B

57${}^{\circ }$

$\because$ AB $\parallel$ DE,
$\angle$BAD + $\angle$EDA = 180${}^{\circ }$
$\Rightarrow$ $\angle$EDA = 180${}^{\circ }$ - 43${}^{\circ }$
$\Rightarrow$ $\angle$EDA = 137${}^{\circ }$......(i)

We know,
$\angle$EDA = $\angle$EDB + $\angle$BDA
$\Rightarrow$ $\angle$BDA = 137${}^{\circ }$ - 57${}^{\circ }$ = 80${}^{\circ }$

We know, from Legendre's theory, that the sum of all the interior angles of a triangle is equal to two right angles.
$\therefore$ $\angle$BDA + $\angle$DBA + $\angle$BAD = 180${}^{\circ }$
$\Rightarrow$ 80${}^{\circ }$ + x + 43${}^{\circ }$=180${}^{\circ }$
$\Rightarrow$ x = 57${}^{\circ }$