Two adjacent angles of a parallelogram are $(3 x - 4)^{\circ} and (3 x + 10)^{\circ}$ . Find the angles of the parallelogram.

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Solution

Given : Two adjacent angles of a parallelogram are $(3 x - 4)^{\circ} and (3 x + 10)^{\circ}$ .

Let $A B C D$ be a parallelogram such that
$∠ A = (3 x - 4)^{\circ} and ∠ B = (3 x + 10)^{\circ}$

We know that,
Sum of any two adjacent angles of a parallelogram is $180^{\circ}$ .
$\Rightarrow ∠ A + ∠ B = 180^{\circ}$
$\Rightarrow (3 x - 4)^{\circ} + (3 x + 10)^{\circ} = 180^{\circ}$
$\Rightarrow (6 x + 6)^{\circ} = 180^{\circ}$
$\Rightarrow 6 x^{\circ} = 174^{\circ}$
$\Rightarrow x^{\circ} = 29^{\circ}$

$∴ ∠ A = (3 x - 4)^{\circ}$
$= 83^{\circ}$
$∠ B = (3 x - 10)^{\circ}$
$= 97^{\circ}$

As, opposite angles of parallelogram ae equal.
$\Rightarrow ∠ A = ∠ C = 83^{\circ} and ∠ B = ∠ D = 97^{\circ}$

Therefore, the angles of the parallelogram are $83^{\circ}, 97^{\circ}, 83^{\circ} and 97^{\circ}$ .

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