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A side of the triangle below has been extended to form an exterior angle.  What is the value of x.

 

 Apr 2, 2021

Best Answer 

 #1
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Let us denote the interior angle(not 114, not x) as y. Because the exterior angle plus the interior angle sum to $180^\circ$, we have $164+y=180$, which gives $y=16^\circ$. Now, we use the formula for the sum of the angles of a triangle. It states that the sum of all the angles in a triangle is equal to $180^\circ$, so we have $16+114+x=180$, which gives $x=180-16-114$, which gives $\boxed{x=50}$

 Apr 2, 2021
 #1
avatar+484 
+1
Best Answer

Let us denote the interior angle(not 114, not x) as y. Because the exterior angle plus the interior angle sum to $180^\circ$, we have $164+y=180$, which gives $y=16^\circ$. Now, we use the formula for the sum of the angles of a triangle. It states that the sum of all the angles in a triangle is equal to $180^\circ$, so we have $16+114+x=180$, which gives $x=180-16-114$, which gives $\boxed{x=50}$

RiemannIntegralzzz Apr 2, 2021

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