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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  

.

 Sep 5, 2021

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