Question

Considers an isosceles trapezoid have one of its interior angle ${110}^o$. If its two non-parallel sides are extended, they will meet at an angle -

• A. ${30}^o$
• B. ${40}^o$
• C. ${130}^o$
• D. ${140}^o$

Answer 1

The correct option is B ${40}^o$

We know: An isosceles trapezoid is formed by cutting an isosceles triangle along a line parallel to the side of the triangle connecting the equal angles of the triangle.

An isosceles trapezoid has one pair of equal non-parallel sides and one pair of parallel sides.

Draw a isosceles trapezoid $EDCB$ with an interior angle ${110}^o$.
let's say $\angle DEB={110}^o.$

Considering BE as transversal to parallel lines ED and BC, $\angle DEB$ and $\angle B$ are supplementary angles.

$\therefore \angle B={180}^o-\angle DEB={70}^o$

The non-parallel lines of an isosceles trapezoid, when extended, always meet at a point, forming an isosceles triangle.
Hence, $\angle B=\angle C={70}^o$

For $△ABC,$
$\angle A+\angle B+\angle C={180}^o$
$\Rightarrow \angle A+{70}^o+{70}^o={180}^o$
$\Rightarrow \angle A={180}^o-{70}^o-{70}^o={40}^o$

$\therefore$ The required angle is ${40}^o.$