Angle sum property of a quadrilateral – The sum of the angles of a quadrilateral is 360˚.
A Quadrilateral is a four-sided enclosed figure.
Properties of Quadrilateral
A quadrilateral has:
- Four Sides (Edges)
- Four Corners (Vertices).
- Four Angles ( Sum of Angles is 360˚ )
Angle sum property of Quadrilateral Examples
Question 1
The three angles of quadrilateral are 60˚ , 70˚ , 90˚ . Find the fourth angle?
Explanation
Let the measure of the fourth angle be x
According to the angle sum property of a Quadrilateral
The sum of all angles of a quadrilateral = 360˚
60˚ + 70˚ + 90˚ + x = 360˚
220˚ + x = 360˚
x = 360˚ – 220˚
x = 140˚
Hence, the fourth angle of the quadrilateral is 140˚
Question 2
If the four angles of quadrilateral are in the ratio of 9 : 8 : 4 : 15, find the measures of each angle?
Explanation
The ratio of the angles of quadrilateral are = 9 : 8 : 4 : 15
Let, the measures of each angle be 9a , 8a , 4a , 15a
According to Angle sum property of a Quadrilateral
The sum of all angles of a quadrilateral = 360˚
9a + 8a + 4a + 15a = 360˚
36a = 360˚
a = 360˚/36
a = 10˚
So, 1st angle = 9a = 9 x 10˚ = 90˚
2nd angle = 8a = 8 x 10˚ = 80˚
3rd angle = 4a = 4 x 10˚ = 40˚
4th angle = 15a = 15 x 10˚ = 150˚
Hence, angles of Quadrilateral are 90˚ , 80˚ , 40˚ and 150˚
Question 3
If the measure of two angles of a quadrilateral are 55˚ and 75˚ and the other two angles are equal, find the measure of each of the equal angles?
Explanation
Let the measure of each of the equal angle be x
According to Angle sum property of a Quadrilateral
The sum of all angles of a quadrilateral = 360˚
55˚ + 75˚ + x + x = 360˚
130˚ + 2x = 360˚
2x = 230˚
x = 230˚/2
x = 115˚
Hence, the measure of equal angles is 115˚
Question 4
If three angles of quadrilateral are equal and the measure of the fourth angle is 30˚ , find the measure of each of the equal angle?
Explanation
Let the measure of each of the equal angle be x
According to Angle sum property of a Quadrilateral
The sum of all angles of a quadrilateral = 360˚
30˚ + x + x + x = 360˚
30˚ + 3x = 360˚
3x = 360˚ – 30˚
3x = 330˚
x = 330˚/3
x = 110˚
Hence, the measure of each equal angle is 110˚