Question

If two adjacent angles i.e., A and B of the parallelogram ABCD are (3x - 4)${}^{\circ }$ and (3x + 16)${}^{\circ }$ respectively, then the measure of angle C is _____ .

• A. 100${}^{\circ }$
• B. 60${}^{\circ }$
• C. 80${}^{\circ }$
• D. 120${}^{\circ }$

Answer 1

The correct option is C 80${}^{\circ }$


Given, ABCD is a parallelogram.
and $\angle A=(3x-4{)}^{\circ }$
$\angle B=(3x+16{)}^{\circ }$

$\therefore$ $\angle A$ + $\angle B$ = 180${}^{\circ }$
[$\because$ Sum of adjacent angles of a parallelogram is 180${}^{\circ }$]

$\Rightarrow 3x^{\circ }-4^{\circ }+3x^{\circ }+{16}^{\circ }={180}^{\circ }$
$\Rightarrow 6x^{\circ }+{12}^{\circ }={180}^{\circ }$
$\Rightarrow 6x^{\circ }={168}^{\circ }$
$\Rightarrow x^{\circ }={28}^{\circ }$

Hence, $\angle A=(3x-4{)}^{\circ }=[(3\times 28)-4{]}^{\circ }={80}^{\circ }$

The opposite angles of a paralleleogram are equal.
Hence, $\angle C$ = $\angle A$ = 80${}^{\circ }$