Question

In parallelogram $ABCD,\angle A=3$ times $\angle B.$ Find all the angles of the parallelogram. In the same parallelogram if $AB=5x-7$ and $CD=3x+1;$ find the length of $CD.$

Answer 1

Let $\angle B=x$

$\angle A=3\angle B=3x$

$AD||BC$

$\angle A+\angle B={180}^o$

$3x+x={180}^o$

$\Rightarrow 4x={180}^o$

$\Rightarrow x={45}^o$

$\angle B={45}^o$

$\angle A=3x=3\times 45={135}^o$

And $\angle B=\angle D={45}^o$

Opposite angles of parallelogram are equal

$\angle A=\angle C={135}^o$

Opposite sides of parallelogram are equal.

$AB=CD$

$5x-7=3x+1$

$\Rightarrow 5x-3x=1+7$

$\Rightarrow 2x=8$

$\Rightarrow x=4$

$CD=3\times 4+1=13$

Hence ${135}^o,{45}^o,{135}^o$ and ${45}^o.$