Question

$\mathrm{ABCD}$ is a trapezium in which $\mathrm{AB}\left|\right|\mathrm{DC}$ and $\angle \mathrm{A}=\angle \mathrm{B}=45º$. Find angles $\angle \mathrm{C}$ and$\angle \mathrm{D}$of the trapezium.

Answer 1

Finding the angles $\angle \mathrm{C}$ and$\angle \mathrm{D}$of the trapezium:

According to given details

$\mathrm{ABCD}$is a trapezium and$\angle \mathrm{A}=\angle \mathrm{B}=45º$

We know that angles opposite to each other in a quadrilateral are supplementary.

So, $\begin{array}{rcl}\angle A+\angle C& =& 180º\end{array}$

$\begin{array}{rcl}& \Rightarrow & 45+\angle C=180\\ & \Rightarrow & \angle C=180–45\\ & \Rightarrow & \angle C=135°\end{array}$

Similarly, $\begin{array}{rcl}\angle B+\angle D& =& 180º\end{array}$

$\begin{array}{rcl}& \Rightarrow & 45+\angle D=180\\ & \Rightarrow & \angle D=180–45\\ & \Rightarrow & \angle D=135°\end{array}$

Therefore the measures of remaining angles are $\angle C=135°,\angle D=135°$