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Angle Sum Property

Theorem 8
The sum of the three angles of a triangle is equal to 180°.
Given: A triangle ABC.
To Prove: ABC + ACB + BAC = 180° or 1 + 2 + 3 = 180°
Construction: Through A, draw a line MN parallel to BC.

Proof: Since BC || MN,
5 = 1 and 4 = 2 ….(Alternate interior angles)
5 + 4 = 1 + 2
Adding 3 on both sides, we get

Þ 5 + 4 + 3 = 1 + 2 + 3
But 5 + 3 + 4 = 180° … (Linear pair axiom)
1 + 2 + 3 = 180°

Thus the sum of the three angles of a triangle is 180°.

 

Question

If the ratio of three angles of a triangle is 2 : 3 : 4, find the angles.

Solution

 


Example:

Solution : Let the measure of three angles of the triangle ABC be 2k, 3k and 4k

2k + 3k + 4k = 180°


               9k = 180°

                 k = 20

Hence the angles of the triangle are 40°, 60° and 80°
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