Angle Sum Property of a Quadrilateral

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˚

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