the angles of a quadrilateral are in the ratio 2:3:5:8
find their size
To find the size of the angles in a quadrilateral, we can use the fact that the sum of the interior angles of a quadrilateral is always 360 degrees.
Let's denote the four angles in the ratio as 2x, 3x, 5x, and 8x. Since the sum of these angles is 360 degrees, we can write the equation:
2x + 3x + 5x + 8x = 360
Simplifying the equation, we get:
18x = 360
Dividing both sides by 18, we find:
x = 360/18 = 20
Now, we can substitute the value of x back into the expressions for the angles to find their sizes:
Angle 1: 2x = 2 * 20 = 40 degrees
Angle 2: 3x = 3 * 20 = 60 degrees
Angle 3: 5x = 5 * 20 = 100 degrees
Angle 4: 8x = 8 * 20 = 160 degrees
Therefore, the sizes of the angles in the quadrilateral are:
Angle 1: 40 degrees
Angle 2: 60 degrees
Angle 3: 100 degrees
Angle 4: 160 degrees
if the smallest is 2x, then
2x+3x+5x+8x = 360
So, find x and you have your answers.