Question

The angles of a quadrilateral are in the ratio of 2:3:5:8. Find the angles of the quadrilateral.
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Answer 1

$\huge{\underbrace{\textsf{\textbf{\color{lightblue}{Answer:-}}}}}$

The ratio of angles of quadrilateral are 2:3:5:8

⇒ Let the four angles be 2x,3x,5x and 8x.

We know, sum of four angles of quadrilateral is 360°

∴ 2x + 3x + 5x + 8x = 360°

⇒18x = 360°

⇒ x = 20°

The angles are,

⇒ 2x = 2×20° = 40°

⇒ 3x = 3×20 = 60°

⇒ 5x = 5×20 = 100 °

⇒ 8x = 8×20° = 160°

∴ The smallest angle of the quadrilateral is 40°.

Answer 2

Given :-

The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8.

To Find :-

What are the angles of the quadrilateral.

Solution :-

Let, the first angles be 2x

Second angles be 3x

Third angles be 5x

And, the fourth angles will be 8x

As we know that,

★ Sum of angles of quadrilateral = 360° ★

According to the question by using the formula we get,

$\sf 2x + 3x + 5x + 8x =\: 360^{\circ}$

$</p><p>\sf 18x =\: 360^{\circ}$

$\sf x =\: \dfrac{\cancel{360^{\circ}}}{\cancel{18}}$

$\sf\bold{\pink{x =\: 20^{\circ}}}$

Hence, the required angles are,

✧ First angles = 2x = 2(20°) = 40°

✧ Second angles = 3x = 3(20°) = 60°

✧ Third angles = 5x = 5(20°) = 100°

✧ Fourth angles = 8x = 8(20°) = 160°

The angles of a quadrilateral is 40°,60°,100° And 160°

${\red{\boxed{\large{\bold{VERIFICATION :-}}}}}$

$\sf 2x + 3x + 5x + 8x =\: 360^{\circ}$

By putting x = 20° we get,

$\sf 40^{\circ} + 60^{\circ} + 100^{\circ} + 160^{\circ} =\: 360^{\circ}$

$\sf 360^{\circ} =\: 360^{\circ}$

➦ LHS = RHS

Hence verified ✓