Find missing angles in triangles and quadrilaterals :
Before look into the examples, we must know the following things about triangles and quadrilaterals.
Triangles 
In a triangle, the sum of interior angles of a triangle is 180 degree.  
Quadrilaterals 
In a quadrilateral, the sum of interior angles of a quadrilateral is 360 degree.  
Trapezium 
The angles at the ends of each nonparallel side are supplementary.  
Isosceles

The angles at the ends of each parallel side are equal.  
Square 
Sum of the angles of a square are equal to 360 degree. Diagonals of a square intersect its right angles,  
Rectangle 
All four angles of a rectangles is right. The sum all of the angles of a rectangle is equal to 360 degrees.  
Parallelogram 
Opposite angles are equal and sum of any two adjacent angles is 180°. The sum of the parallelogram angles is equal to 360 degrees.  
Rhombus 
Opposite angles are equal and sum of any two adjacent angles is 180°. Diagonals bisect each other at right angles. 
Example 1 :
Find the missing angles of the following triangle
Solution :
In any triangle, the sum of interior angles of the triangles is 180 degree.
From the given triangle, we come to know that angle B is 90 degree.
∠A + ∠B + ∠C = 180°
40° + 90° + ∠C = 180°
130° + ∠C = 180°
∠C = 180°  130°
∠C = 50°
Hence the missing angle is 50°.
Example 2 :
Find the missing angles of the following trapezium
Solution :
In a trapezium, the angles at the ends of each nonparallel side are supplementary.
∠C + ∠D = 180°
120° + ∠D = 180°
∠D = 180°  120°
∠D = 60°
Hence the missing angle is 60°.
Example 3 :
Find the missing angles of the following quadrilateral
Solution :
In a quadrilateral, the sum of interior angles of a quadrilateral is 360 degree.
∠D + ∠E + ∠F + ∠G = 360°
87° + 110° + 65° + ∠G = 360°
262° + ∠G = 360°
∠G = 360°  262°
∠G = 98°
Example 4 :
Find the missing angles of the following square
Solution :
In a square all angles are right angles.
∠S = 16 x  6 = 90°
16x  6 = 90°
16x = 90° + 6
16x = 96°
Divide by 16 on both sides
16x/16 = 96/16
x = 6°
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