The angles of a quadrilateral in the ratio 2:3:4:1 . Find the measure of each angle of the quadrilateral.
they add up to 360.
Divide 360 into 2+3+4+1=10 parts, and each part is 36. So, the angles are
72:108:144:36
To find the measure of each angle of the quadrilateral, we need to understand that the sum of the angles in any quadrilateral is always equal to 360 degrees.
Let's denote the angles as 2x, 3x, 4x, and x.
According to the given ratio, the angles are in the ratio 2:3:4:1.
So, the sum of these four angles can be expressed as:
2x + 3x + 4x + x = 360
Combining like terms, we have:
10x = 360
Now, to solve for x, we divide both sides of the equation by 10:
10x/10 = 360/10
x = 36
Now, we can find the measure of each angle by substituting the value of x back into the expressions for the angles:
Angle 1: 2x = 2 * 36 = 72 degrees
Angle 2: 3x = 3 * 36 = 108 degrees
Angle 3: 4x = 4 * 36 = 144 degrees
Angle 4: x = 36 degrees
Therefore, the four angles in the given quadrilateral measure 72 degrees, 108 degrees, 144 degrees, and 36 degrees, respectively.