Question

pls solve this.......​

Answer 1

GIVEN:-

An angle in a quadrilateral is 72°.

Other three angles are in the ratio of 5:6:7.

To Find:-

All the angles of the quadrilateral.

SOLUTION.

A quadrilateral also has four angles formed by its four sides. Below are some examples of quadrilaterals. Notice that each figure has four straight sides and four angles. The sum of the interior angles of any quadrilateral is 360°.

According to the question,

Let the three angles be 5x, 6x, 7x.

Other angle is 72°.

$\large\Longrightarrow{\sf{5x+6x+7x+72\degree=360\degree}}$

$\large\Longrightarrow{\sf{18x=360-72}}$

$\large\Longrightarrow{\sf{18x=288}}$

$\large\Longrightarrow{\sf{x=\frac{288}{18}}}$

$\large\therefore\boxed{\sf{x=16}}$

So the angles are:-

$\large{\sf{5x=5\times16=80\degree}}$

$\large{\sf{6x=6\times16=96\degree}}$

$\large{\sf{7x=7\times16=112\degree}}$

Let's verify it:-

As we know sum of interior angles of a quadrilateral is 360°.

Therefore,

By adding 72°,80°,96°,112° we get 360°.

$\large\therefore\boxed{\sf{\blue{The \:four\: angles \:are:- \:72\degree,\:80\degree,\:96\degree \:and\: 110\degree}}}$

Answer 2

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