Angle Sum Property


ABOUT:

In this section, we shall state and prove angle sum property of triangles. Here we will discuss some problems based on it.
Theorem 1: The sum of all the angles of a triangle is 1800

Given : 

A triangle ABC.
To Prove:

∠A + ∠B + ∠C= 1800
Construction: 

Draw CE such that CE || AB

Statements

Reasons

1)BA || CE

1) By Construction

2) ∠A = ∠ACE

2) Alternate interior angle

3) ∠B = ∠DCE

3) Corresponding angles

4)∠A + ∠B = ∠ACE + ∠DCE

4) Addition property of (1) and (2)

5) ∠A + ∠B + ∠ACB = ∠ACE + ∠DCE + ∠ACB

5) Adding ∠ACB to both sides

6) ∠A + ∠B + ∠C = 1800

6) Straight line angles.

DEMONSTRATION:

1). Two angles of a triangle are of measures 75 0 and 35 0 . Find the measures of the third angle.
Solution : 
Let ABC be a triangle such that ∠B 75 0 and ∠C = 35 0 . Then, we have to find the measure of the third angle A.
By angle sum property of triangles, 

∠A + ∠B + ∠C = 180

∠A + 75 + 35 = 180 

∠A + 110 = 180 
∠A = 180 -110, ∠A = 70 0