Question

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

A
143
B
153
C
163
D
173

Solution

## The correct option is A $$143$$Here, $$ABCD$$ is a parallelogramLet $$\angle A=(3x-2)^o$$ 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 $$143^o$$Maths

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