Question

Ankush prepared a poster in the form of a parallelogram , as in the figure.
(i) If $\angle A=(5x+7{)}^{\circ }$ and $\angle B=(3x-3{)}^{\circ }$, find all the angles of parallelogram ABCD. ---[2 marks]
(ii) Which mathematical concept is used in this question? ---[1 mark]

Answer 1

(i) Since sum of adjacent angles of a parallelogram is ${180}^{\circ }$

$\therefore$ We have $\angle A+\angle B={180}^{\circ }$
$\Rightarrow 5x+7+3x-3={180}^{\circ }$
$\Rightarrow 8x+4={180}^{\circ }$
$\Rightarrow 8x={176}^{\circ }$
$\Rightarrow x=\frac{{176}^{\circ }}{8}={22}^{\circ }$
$\therefore \angle A=(5x+7{)}^{\circ }=(5\times 22+7{)}^{\circ }={117}^{\circ }$
$\angle B=(3x-3{)}^{\circ }=(3\times 22-3{)}^{\circ }={63}^{\circ }$
$\angle C=\angle A={117}^{\circ }$ (opposite angles of parallelogram) -----[ 1 mark]
$\angle D=\angle A={63}^{\circ }$ (opposite angles of parallelogram) -----[ 1 mark]

(ii) Properties of a parallelogram -----[ 1 mark]