AMC 8 Daily Practice - Triangle Properties

Complete problem set with solutions and individual problem pages

Problem 1 Easy

As shown in the figure, \angle A = 30^\circ, \angle B = 60^\circ, and \angle C = 20^\circ. What is the value of x?

  • A.

    99^\circ

  • B.

    105^\circ

  • C.

    110^\circ

  • D.

    120^\circ

  • E.

    130^\circ

Answer:C

Connect BD.

In \triangle ABD, \angle ADB = 180^\circ - 30^\circ - \angle ABD = 150^\circ - \angle ABD.

In \triangle BCD, \angle BDC = 180^\circ - 20^\circ - \angle CBD = 160^\circ - \angle CBD.

Then, \angle ADC = 360^\circ - \angle ADB - \angle BDC

= 360^\circ - (150^\circ - \angle ABD) - (160^\circ - \angle CBD)

= 360^\circ - 150^\circ + \angle ABD - 160^\circ + \angle CBD

= 110^\circ

Thus, x = 110^\circ.

Related Problems
Problem 2 AMC 8 Daily Practice - Triangle Properties
Problem 3 AMC 8 Daily Practice - Triangle Properties
Problem 4 AMC 8 Daily Practice - Triangle Properties
Problem 5 AMC 8 Daily Practice - Triangle Properties
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