AMC 8 Daily Practice - Triangle Properties

Complete problem set with solutions and individual problem pages

Problem 3 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 \angle a, \angle b, and \angle c, where \angle a < \angle b < \angle c.

According to the problem, we know that \angle c = 5\angle a and \angle b = 3\angle a.

Thus, the ratio of the angles is \angle a : \angle b : \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: \angle c = 180^\circ \div (1 + 3 + 5) \times 5 = 100^\circ.

Related Problems
Problem 1 AMC 8 Daily Practice - Triangle Properties
Problem 2 AMC 8 Daily Practice - Triangle Properties
Problem 4 AMC 8 Daily Practice - Triangle Properties
Problem 5 AMC 8 Daily Practice - Triangle Properties
Think Academy Powered by ChatGPT