AMC 10 Daily Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 3 Easy

In isosceles \triangle ABC with AB = AC, point D lies on \overline{AC} such that \overline{BD} \perp \overline{AC}. Given that \triangle ABD is isosceles, what is the degree measure of \angle C?

  • A.

    45^{\circ}

  • B.

    60^{\circ}

  • C.

    67.5^{\circ}

  • D.

    72^{\circ}

  • E.

    75^{\circ}

Answer:C

Since \triangle ABD is isosceles with \overline{BD} \perp \overline{AC}, we know that \triangle ABD is an isosceles right triangle. This gives the measure of \angle C is 67.5^{\circ} in isosceles \triangle ABC.

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Problem 1 AMC 10 Daily Practice Round 3
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