Question

FIND THE MEASURES OF THE FOUR ANGLES OF A QUADRILATERAL IF THEY ARE IN RATIO 2:4:6:8.​

Answer 1

Step-by-step explanation:

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Answer 2

$\large \pmb{ \sf{ \underline{ \underline{Given : - }}}}$

• Measure of four angles of a quadrilateral are in ratio $\sf{2:4:6:8}$

$\large \pmb{ \sf{ \underline{ \underline{To \: Find : - }}}}$

• Measure of four angles.

Step-by-step Explaination

Now, we will consider 'x' common in given ratios.

$\sf{ \therefore \: First \: angle \twoheadrightarrow 2x }$

$\sf{ Second \: angle \twoheadrightarrow 4x}$

$\sf{ Third \: angle \twoheadrightarrow 6x}$

$\sf{ Fourth \: angle \twoheadrightarrow 8x}$

Now,

$\pmb{ \boxed{ \sf{ \underline{we \: know \: that \: - }}}}$

By the angle sum property, Sum of all interior angles in a quadrilateral is equal to 360°.

So,

$\twoheadrightarrow \sf{2x + 4x + 6x + 8x = 360 \degree}$

$\twoheadrightarrow \sf{20x = 360 \degree}$

$\twoheadrightarrow \sf{x = \frac{360 \degree}{20}}$

$\large \pmb \sf{ = \pink{18 \degree}}$

Now, Multiply all the given ratios with 18.

$\twoheadrightarrow \sf{2x = 2 \times 18 = 36 \degree}$

$\twoheadrightarrow \sf{4x = 4 \times 18 = 72 \degree}$

$\twoheadrightarrow \sf{6x = 6 \times 18 = 108 \degree}$

$\twoheadrightarrow \sf{8x = 8 \times 18 = 144 \degree}$

❝ Therefore, Measure of the four angles of a quadrilateral are 36°, 72°, 108°, 144°. ❞

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