The angles of a quadrilateral are in the ratio 2: 3: 5: 8. Find the measure of each angles.

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Step-by-step explanation:

Let's call the angles 2x, 3x, 5x and 8x and since the sum of angles in a quadrilateral is 360 degrees we can write:

2x + 3x + 5x + 8x = 360

18x = 360

x = 20 which means the angle measures are 40°, 60°, 100° and 160°

40°,60°,100° and 160°

Step-by-step explanation:

First add all the ratio's together

2 + 3 + 5 + 8 = 5 + 13 = 18

Now we utilise the fact that angles in quadrilaterals add up to 360. We form an equation like this 18x = 360 to find the value of x and then substitute back into the ratio's

18x = 360

→ Divide both sides by 18 to isolate x

x = 20

Multiply 20 by each of the ratio's to find the angles of this quadrilateral

2 * 20 = 40

3 * 20 = 60

5 * 20 = 100

8 * 20 = 160

So the angles of a quadrilateral with the ratio of 2: 3 : 5 : 8 is 40,60,100 and 160