Math, asked by navneet1306, 5 months ago


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

Answers

Answered by bhaskar8014
2

Answer:

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Answered by Anonymous
15

Answer:

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}

\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°

\therefore 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

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