Question

in a parallelogram ABCD the ratio of the measure of angle A and angle B are 1:3 find the measure of all the angle

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Answer 1

$\large{\red{\underline{\underline{\bold{Given:-}}}}}$

• The ratio of the measure of angle A and B are in the ratio 1 : 3

$\large{\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The measure of all the angles of the parallelogram

$\large{\green{\underline{\underline{\bold{Solution:-}}}}}$

$\sf Let \: the \: measure \: of \: \angle A \: and \: \angle B \: be \: x \: and \: 3x$

We know that the sum of adjacent angles in a parallelogram is 180°

$\rightarrow\sf \angle A \: + \: \angle B = 180 \degree$

$\sf \rightarrow x + 3x\: = 180 \degree$

$\sf \rightarrow 4x\: = 180 \degree$

$\sf \rightarrow x\: = \dfrac{180}{4}$

$\sf \rightarrow x\: = 45\degree$

$\sf \rightarrow \angle A = 45 \degree$

$\sf \rightarrow 3x = 45 \times 3 = 135 \degree$

$\sf \rightarrow \angle B = 135 \degree$

$\sf \rightarrow \angle A = \angle C = 45 \degree$ (Opposite angles of parallelogram are equation)

$\sf \rightarrow \angle B = \angle D = 135 \degree$

The measure of all the angles of parallelogram are:-

• ∠A = 45°

• ∠B = 135°

• ∠C = 45°

• ∠D = 135°

Answer 2

Answer:

In a parallelogram the sum of adjacent angles is 180°

Therefore, sum of angles a and b is 180°

Ratio of angles a and b is 1:3

Sum of ratio is 4

Therefore angle a = 1/4(180)

= 45°

Angle b = 3/4(180) = 135°

Step-by-step explanation: