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# geometry

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Two of the exterior angles of a triangle are 158 degrees and 93 degrees Find the third exterior angle, in degrees.

Sep 4, 2021

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Two of the exterior angles of a triangle are 158 degrees and 93 degrees Find the third exterior angle, in degrees.

The easy way:

By knowing that the sum of the exterior angles of any convex polygon is 360 degrees.

Therefore, the exterior angle at the third vertex can be found as 360o – (158o + 93o)  =  109o

The lengthy way:

Call the triangle vertices A, B, and C.  Extend one side of the triangle at each vertex.

A straight line is 180o so find the supplementary angle at each vertex to determine the size of the third angle.

Call A the vertex with exterior angle 158o  so the interior angle at vertex A is 180o – 158o = 22o.

Call B the vertex with exterior angle   93o  so the interior angle at vertex B is 180o –   93o = 87o.

So the interior angles of the triangle are Co and 22o and 87o.

The sum of the interior angles of a triangle is 180o so angle C is 180o – (22o + 87o)  =  71o

The exterior angle at C is the supplementary angle of 71o which is 180o – 71o  =  109o   same as above

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Sep 5, 2021