Sum of angles of a quadrilateral are discussed here. We have now two triangles in the below figure.
We know, the sum of the angles of a triangle = 180°
Since there are two triangles,
therefore, the sum of two triangles is 180° + 180° = 360°
Note: The sum of the four angles is 360°.
For Example:
1. In a quadrilateral ABCD, ∠A = 100°, ∠B = 105° and ∠C = 70°, find ∠D.
Solution:
Here the sum of the four angles
or, ∠A + ∠B + ∠C + ∠D = 360°
We know, ∠A = 100°, ∠B = 105° and ∠C = 70°
or, 100° + 105° + 70° + ∠D = 360°
or, 275° + ∠D = 360°
∠D = 360° - 275°
Therefore, ∠D = 85°
2. Find the measure of the missing angles in a parallelogram, if ∠A = 70°.
Solution:
We know the opposite angles of a parallelogram are equal.
So, ∠C will also measure 70°
Sum of angles = 360°
∠A + ∠B + ∠C + ∠D = 360°
or, 70° + ∠B + 70° + ∠D = 360° (We know, ∠A = ∠C )
or, ∠B + ∠D + 140° = 360°
or, ∠B + ∠D = 360° - 140°
or, ∠B + ∠D = 220°
But ∠B = ∠D (Because opposites angles of a parallelogram are equal)
∠B = ∠D
= 220° ÷ 2
= 110°
Therefore, ∠B = 110°, ∠C = 70° and ∠ D = 110°
Construction of Perpendicular Lines by using a Protractor.
Sum of Angles of a Quadrilateral.
Practice Test on Quadrilaterals.
5th Grade Geometry Page
5th Grade Math Problems
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