Question

In a trapezium, two adjacent angles are ${50}^o$ and ${70}^o$. Find the remaining two angles.

Answer 1

In trapezium one pair of opposite sides are parallel.

Let $ABCD$ is trapezium having, $AB\parallel CD$

Let $\angle A={50}^o.$ and $\angle B={70}^o.$

Since, $AB\parallel CD$ and $AD$ is a transversal. Then,

$\Rightarrow$ $\angle A+\angle D={180}^o$

$\Rightarrow$ ${50}^o+\angle D={180}^o$

$\therefore$ $\angle D={130}^o.$

Since, $AB\parallel CD$ and $BC$ is a transversal. Then,

$\Rightarrow$ $\angle B+\angle C={180}^o.$

$\Rightarrow$ ${70}^o+\angle C={180}^o$

$\Rightarrow$ $\angle C={110}^o$

$\therefore$ Measure of remaining two angles are ${130}^o$ and ${110}^o.$