The figure below is a parallelogram with two angles given in terms of x. Determine the value of x.

9

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10

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20

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22

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24

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Solution

The correct option is C $22$
We know that, adjacent angles of a parallelogram are supplementary; that is, they add to $180^{o}$ .
Use this to set up an equation, and then solve it for $x$ .
$∴ (4 x + 12) + (3 x + 14) = 180$
$\Rightarrow 7 x + 26 = 180$
$\Rightarrow 7 x = 154$
$\Rightarrow x = 22$
Hence, the value of $x$ is $22$ .

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