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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 $$45^o.$$

1779319_1839076_ans_3deb1aec90144371af1bace03eebb6eb.png

Mathematics

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