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.
(ii) Which mathematical concept is used in this question?
(iii) By writing a slogan on the poster, which value is depicted by Ankush? [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks


(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)
$\angle D=\angle A={63}^{\circ }$ (opposite angles of parallelogram)

(ii) Properties of a parallelogram

(iii) Energy conservation is very much necessary to have a happy and prosperous future.