Question

The angles of a quadrilateral are in the ratio 4:5:7:8. Find the measure of each of these angles.

Answer 1

Answer:

the angles of a given quadrilateral are:  60° , 75° , 105° , 120°

Step-by-step explanation:

given that:

The angles of a quadrilateral are in the ratio 4:5:7:8

let 'x' be the common multiple of given ratio.

since the sum of angles of a quadrilateral is 360°

sum up all the given angles.

4x + 5x + 7x + 8x = 360°

x(4 + 5+ 7+ 8) = 360°

x( 9 + 15) = 360°

x(24) = 360°

x = (360) / (24)

x = (30) / (2)

x = 15°

so 4x = (4)(15) = 60°

5x = (5)(15) = 75°

7x = (7)(15) = 105°

8x = (8)(15) = 120°

the angles of a given quadrilateral are:

4x , 5x , 7x , 8x

⇒ 60° , 75° , 105° , 120°

Answer 2

Hi! Hope this helps!!

Answer: 60, 75, 105, 120

Step-by-step explanation:

We know that the four angles of a quadrilateral add up to 360.

And that any numbers in a ratio are all multiplied by the same number.

So,

  4 + 5 + 7 + 8 = 360

= 24 = 360

= = 360 ÷ 24

= = 15

Now, we put this solution to find the measure of the angles.

4 = 4 × 15 = 60

5 = 5 × 15 = 75

7 = 7 × 15 = 105

8 = 8 × 15 = 120

And we've got our answer!

                                                          P.S. Please mark me as Brainliest! Thnx!