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

Answer 1

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

Opposite angles of a parallelogram are equal.
$$\begin{gathered} \therefore 3x-2=50-x \\ \Rightarrow 3x+x=50+2 \\ \Rightarrow 4x=52 \\ \Rightarrow x=13 \end{gathered}$$

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