Question

$\text{In parallelogram ABCD,}\angle A=3times\angle B.$

$\text{Find all the angles of the parallelogram.}$

$\text{In the same parallelogram,~if}AB=5x-7and$

$CD=3x+1;\text{find the length of CD.}$

Answer 1

$Let\angle B=x\therefore \angle A=3\angle B=3x\because AD||BC\therefore \angle A+\angle B={180}^{\circ }3x+x={180}^{\circ }4x={180}^{\circ }\therefore x={45}^{\circ }\therefore \angle B={45}^{\circ }\&\angle A=3x=3\times 45={135}^{\circ }\because \text{opposite angle of}||\text{gm are equal.}\therefore \angle A=\angle C={135}^{\circ }and\angle B=\angle D={45}^{\circ }\because \text{opposite sides of}||\text{gm are equal.}\therefore AB=CD\therefore 5x-7=3x+15x-3x=1+72x=8x=4CD=3\times 4+1=13Hence{135}^{\circ },{45}^{\circ },{135}^{\circ }and{45}^{\circ };13$