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# Exterior Angles

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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

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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