Question

Project - Verify the sum of exterior angle
a Quadrilletral is 360°.
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Answer 1

Answer:

Theorem: If any side of a triangle is extended, then the exterior angle so formed is the sum of the two opposite interior angles of the triangle.

Exterior Angle Property of a Triangle

In the given figure, the side BC of ∆ABC is extended. The exterior angle ∠ACD so formed is the sum of measures of ∠ABC and ∠CAB.

Proof: From figure 3, ∠ACB and ∠ACD forms a linear pair since they represent the adjacent angles on a straight line.

Thus, ∠ACB + ∠ACD = 180° ……….(2)

Also, from the angle sum property it follows that:

∠ACB + ∠BAC + ∠CBA = 180° ……….(3)

From equation (2) and (3) it follows that:

∠ACD = ∠BAC + ∠CBA