Question

Angles In Quadrilateral Are x, 2x,2x,3x. Find The Measure Of Exterior Angle Of Smallest Angle

Answer 1

To find :-

The smallest exterior angle of the given sum.

Given :-

The measures of a four angles of a quadrilateral are respectively.

Solution :

Step-by-step explanation:

So, First Let's find the value of x

Here, the unknown angles are x , 2x , 2x and 3x

We know that,

The sum of all the angles of a quadrilateral is 360°

The angles of quadrilateral are

By the problem,

$\implies$ x + 2x + 2x + 3x = 360

$\implies$ x + 7x = 360

$\implies$ 8x = 360

$\implies$ x = 45°

So,

x = 45°

2x = 2 × 45 = 90°

2x = 2 × 45 = 90°

3x = 3 × 45 = 135°

Now, Verification:

The angles of the quadrilateral are:-

90° , 45° , 90° and 135°

$\therefore$90+45+90+135 = 360

$\implies$180+45+135 = 360

$\implies$360 = 360

$\green{Hence, L.H.S = R.H.S}$

The biggest interior angle will be with the smallest exterior angle.

Therefore, the smallest exterior angle of it is 135°