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Question

The opposite angles of a parallelogram are $$(3x - 2)^{\circ}$$ and $$(x + 48)^{\circ}$$. Find the measure of each angle of the parallelogram.


Solution

Given opposite angles of parallelogram are $$(3x-2)^{0}$$ and $$(x+48)^{0}$$ 

We know opposite angles of  parallelogram are equal 

$$\therefore 2(3x-2)+2(x+48)=360$$

$$\Rightarrow 6x-4+2x+96=360$$

$$\Rightarrow 6x+2x=360+4-96$$

$$\Rightarrow 8x=268$$

$$\Rightarrow x=33.5$$

Then $$3x-2=3\times 33.5-2=100.5-2=98.5$$

And $$x+48=33.5+48=81.5$$

Then angle are $$98.5,81.5,98.5,81.5$$

Mathematics

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