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Ex.8.1 Q1 Quadrilaterals Solution - NCERT Maths Class 9

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Question

The angles of quadrilateral are in the ratio \(3:5:9:13\). Find all the angles of the quadrilateral.

 Video Solution
Quadrilaterals
Ex 8.1 | Question 1

Text Solution

What is known?

The angles of quadrilateral are in the ratio \(3:5:9:13.\)

What is unknown?

All the angles of the quadrilateral.

Reasoning:

Sum of angles in any quadrilateral is \(360\) degree.

Steps:

Let the common ratio between the angles be \(x\).

Therefore, the angles will be \(3x\), \(5x\), \(9x\), and \(13x\) respectively. according to the given ratio.

As the sum of all interior angles of a quadrilateral is \(360^\circ\) ,

\[\begin{align} ∴\;3 x+5 x+9 x+13 x &=360^{\circ}\\30 x&=360^{\circ} \\x&=12^{\circ}\end{align}\]

Hence, the angles are

\[\begin{align}3 x&=3 \times 12=36^{\circ} \\ 5 x&=5 \times 12=60^{\circ} \\ 9 x&=9 \times 12=108^{\circ} \\ 13 x&=13 \times 12=156^{\circ}\end{align}\]

 Video Solution
Quadrilaterals
Ex 8.1 | Question 1