Question

In parallelogram ABCD, $\angle$A is 3 times $\angle$B. Find all the angles of the parallelogram. In the same parallelogram of 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
$\angle A+\angle B={180}^{\circ }3x+x={180}^{\circ }\Rightarrow 4x={180}^{\circ }\Rightarrow x={45}^{\circ }\angle B={45}^{\circ }\angle A=3x=3\times 45={135}^{\circ }And\angle B=\angle D={45}^{\circ }$
Opposite angles of parallelogram are equal.
$\angle A=\angle C={135}^{\circ }$
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
$Henceanglesare{135}^{\circ },{45}^{\circ },{135}^{\circ }and{45}^{\circ },andCD=13$