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 $$CD.$$

Solution

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 $$45^o.$$Mathematics

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