AMC 8 Daily Practice Round 7

Complete problem set with solutions and individual problem pages

Problem 12 Easy

In a triangle, the largest angle is 5 times the smallest angle, and the other angle is 3 times the smallest angle. What is the degree measure of the largest angle?

  • A.

    90

  • B.

    92.5

  • C.

    100

  • D.

    102.5

  • E.

    112.5

Answer:C

Let the three angles of the triangle be m\angle A, m\angle B, and m\angle C, where m\angle A < m\angle B < m\angle C.

According to the problem, we know that m\angle C = 5m\angle A and m\angle B = 3\angle a.

Thus, the ratio of the angles is m\angle A : m\angle B : m\angle C = 1 : 3 : 5.

Since the sum of the interior angles of a triangle is 180^\circ, the measure of the largest angle \angle C is: m\angle C = 180^\circ \div (1 + 3 + 5) \times 5 = 100^\circ.

Related Problems
Problem 10 AMC 8 Daily Practice Round 7
Problem 11 AMC 8 Daily Practice Round 7
Problem 13 AMC 8 Daily Practice Round 7
Problem 14 AMC 8 Daily Practice Round 7
Think Academy Powered by ChatGPT