The measures of the four angles of quadrilateral ABCD are 36°, 72°, 108° and 144°
Step-by-step explanation:
A polygon has three or more sides.
Example:
Triangle has 3 sides
Square has 4 sides
Pentagon has 5 sides and so on.
27)
In a quadrilateral ABCD, the measure of ZA, ZB, ZC and ZD are the ratio 1 : 2 : 3 : 4
We know,
sum of all the interior angles of a quadrilateral is 360°
So,
x + 2x + 3x + 4x = 360°
10x = 360°
x = 36°
Thus, the measure of four angles would be:
x = 36°
2x = 2 X 36° = 72°
3x = 3 X 36° = 108°
4x = 4 X 36° = 144°
Therefore, the measures of the four angles of quadrilateral ABCD are 36°, 72°, 108° and 144°