Ankush prepared a poster in the form of a parallelogram, as in the figure.
(i) If $∠ A = (5 x + 7)^{\circ}$ and $∠ B = (3 x - 3)^{\circ}$ , 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]

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Solution

Concept: 2 Marks
Application: 2 Marks

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

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

(ii) Properties of a parallelogram

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

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Similar questions

∠ A = (5 x + 7)^{\circ}

∠ B = (3 x - 3)^{\circ}

$In parallelogram ABCD, ∠ A = 3 t i m e s ∠ B .$

$Find all the angles of the parallelogram.$

$In the same parallelogram,~if A B = 5 x - 7 a n d$

$C D = 3 x + 1; find the length of CD.$

∠ A = 3 ∠ B

= 5 x - 7

C D = 3 x + 1

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