Question

The measures of a four angles of a quadrilateral are 2x+10, 3x+15, 4x-30 and 2x -20 respectively . Then find the smallest exterior angle of it ​

Answer 1

(2x+10)+(3x+15)+(4x-30)+(2x-20)=360

11x-25=360

11x=385

X=385/11

=35.

Answer 2

The smallest exterior angle of it is 120°.

Step-by-step explanation:

Given : The measures of a four angles of a quadrilateral are 2x+10, 3x+15, 4x-30 and 2x -20 respectively.

To find : The smallest exterior angle of it ​?

Solution :

The sum of all the angles of a quadrilateral is 360 degree.

So,

$2x+10+3x+15+4x-30+2x -20=360$

$11x-25=360$

$11x=385$

$x=\frac{385}{11}$

$x=35$

The angles of quadrilateral are

$2x+10=2(35)+10=80$

$3x+15=3(35)+15=120$

$4x-30=4(35)-30=110$

$2x-20=2(35)-20=50$

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

Therefore, the smallest exterior angle of it is 120°.

#Learn more

The angles of quadrilateral are in the ratio 2:3:4:6. find the measure of each of the four angles.

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