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Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. The measures of all its angles are
(a) 97°, 83°, 97°, 83°
(b) 37°, 143°, 37°, 143°
(c) 76°, 104°, 76°, 104°
(d) none of these

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Solution

(b) 37^o, 143^o, 37^o 143^o

Opposite angles of a parallelogram are equal.
$∴ 3 x - 2 = 50 - x \Rightarrow 3 x + x = 50 + 2 \Rightarrow 4 x = 52 \Rightarrow x = 13$

Therefore, the first and the second angles are:
${(3 x - 2)}^{\circ} = {(2 \times 13 - 2)}^{\circ} = 37^{\circ} {(50 - x)}^{\circ} = {(50 - 13)}^{\circ} = 37^{\circ}$
Sum of adjacent angles in a parallelogram is $180^{\circ}$ .
Adjacent angles = $180^{\circ} - 37^{\circ} = 143^{\circ}$

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