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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
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