geometry

 

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 360^o – (158^o + 93^o)  =  109^o  

 

The lengthy way:  

 

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

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

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

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

 

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

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

 

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

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