Question

The measures of the angles of a quadrilateral are 3:8:7:2 find the measure of each angle

Answer 1

Angle 1= 54°

Angle 2= 144°

Angle 3 = 126°

Angle 4 = 36°

Explanation:

We are given measures of the angles of a quadrilateral are 3:8:7:2

Let the common ratio = x

The angles will be:

Angle 1= 3x,

Angle 2= 8x,

Angle 3 =7x

Angle 4 =2x

We know that sum of all angles of quadrilateral = 360°

We can write as:
`3x+8x+7x+2x=360`

Solving to find x,

`3x+8x+7x+2x=360\\20x=360\\x=(360)/(20)\\x=18`

We get value of x = 18

Now, finding angles:

Angle 1= 3x = 3(18) = 54°

Angle 2= 8x = 8(18) = 144°

Angle 3 =7x = 7(18) = 126°

Angle 4 =2x = 2(18) = 36°