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 180^{0}
Given :
A triangle ABC. To Prove:
∠A + ∠B + ∠C= 180^{0} 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 = 180^{0}

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}