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Use the Exterior Angle Theorem to show that the sum of the measures of two interior...

Use the Exterior Angle Theorem to show that the sum of the measures of two interior angles of a triangle is always less than 180 degrees.

Can not use that the sum of angles is 180 degrees.

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Answer #1

Let ABC be a triangle as shown in figure below. Draw lines AD and CE parallel to the sides BC and BA respectively. Extend Side BA to point F.

Now  BAC and BCA are interior angles and CAF is an exterior angle at vertex A.

Hence, we have

But, as is a straight angle and for non-trivial triangles therefore

o.

Hence, the theorem.

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