Talk:2021 Fall AMC 10A Problems/Problem 7

Solution 2

Note that $\angle ADC = 90$ , meaning that the reflex of $\angle ADE = 90+110=200^\circ$ , so $\angle ADE = 360-200=160^\circ$ . It is given that $\triangle DEF$ has two sides of equal length, so it is isosceles, thus having two congruent angles.

The sum of these two angles is $180-160=20^\circ$ , so the measure of both $\angle DFE$ and angle $\angle FED$ is $10^\circ$ . Since $\angle AFE$ is the supplement to $\angle DFE$ , and $\angle DFE = 10^\circ$ , $\angle AFE = 180-10 = \boxed{\textbf{(D)}170}$ degrees.

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Talk:2021 Fall AMC 10A Problems/Problem 7

Solution 2