2012 CEMC Gauss (Grade 7) Problems/Problem 5

Problem

Two straight lines intersect as shown.

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The measure of the angle marked $\boxed { }$ is

$\text{ (A) }\ 60^{\circ} \qquad\text{ (B) }\ 120^{\circ} \qquad\text{ (C) }\ 30^{\circ} \qquad\text{ (D) }\ 300^{\circ} \qquad\text{ (E) }\ 180^{\circ}$

Solution 1

Since $120^{\circ}$ degrees and the missing angle forms a straight angle, we have:

$120^{\circ} + \boxed { } = 180^{\circ}$

Thus, $\boxed { } = \boxed {{\textbf (A) } 60^{\circ}}$

Solution 2

Since the $60^{\circ}$ angle and the missing angle are vertical angles, they are equal to each other.

Thus, $\boxed { } = \boxed {{\textbf (A) } 60^{\circ}}$

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2012 CEMC Gauss (Grade 7) Problems/Problem 5

Problem

Solution 1

Solution 2