Question:
Mark (✓) against the correct answer:
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
Solution:
(b) 37o, 143o, 37o 143o
Opposite angles of a parallelogram are equal.
$\therefore 3 x-2=50-x$
$\Rightarrow 3 x+x=50+2$
$\Rightarrow 4 x=52$
$\Rightarrow x=13$
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 $=180^{\circ}-37^{\circ}=143^{\circ}$