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Question

Measures of opposite angles of parallelogram are $$(3x-2) ^{\circ} $$ and $$(50-x) ^{\circ} $$. Find the measure of its other angles.


A
143
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B
153
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C
163
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D
173
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Solution

The correct option is A $$143$$

Here, $$ABCD$$ is a parallelogram
Let $$\angle A=(3x-2)^o$$ and $$C=(50-x)^o$$
We know that in parallelogram opposite angles are equal.
$$\therefore$$  $$\angle A=\angle C$$
$$\Rightarrow$$  $$3x-2=50-x$$
$$\Rightarrow$$  $$4x=52$$
$$\Rightarrow$$  $$x=13$$
$$\Rightarrow$$  $$\angle A=(3x-2)^o=(3\times 13-2)^o=37^o$$
In parallelogram sum of adjacent angles are supplementary.
$$\therefore$$  $$\angle A+\angle B=180^o$$
$$\Rightarrow$$  $$37^o+\angle B=180^o$$
$$\therefore$$  $$\angle B=143^o$$
Hence other two equal opposite angles are $$143^o$$

1256045_1378964_ans_a209123bdc4648f19b6f9aaa66e8de28.jpeg

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