2021 AMC 10 A Fall

Complete problem set with solutions and individual problem pages

Problem 7 Easy

As shown in the figure below, point E lies on the opposite half-plane determined by line C D from point A so that \angle C D E=110^{\circ}. Point F lies on \overline{A D} so that D E=D F, and A B C D is a square. What is the degree measure of \angle A F E ?(2021 AMC Fall 10A, Question #7)

  • A.

    160

  • B.

    164

  • C.

    166

  • D.

    170

  • E.

    174

Answer:D

By angle subtraction, we have \angle A D E=360^{\circ}-\angle A D C-\angle C D E=160^{\circ}. Note that \triangle D E F is isosceles, so \angle D F E=\frac{180^{\circ}-\angle A D E}{2}=10^{\circ}. Finally, we get \angle A F E=180^{\circ}-\angle D F E= (D) 170 degrees.

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