Art of Problem Solving

2012 CEMC Gauss (Grade 7) Problems/Problem 5: Difference between revisions

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==Problem==
==Problem==
Two straight lines intersect as shown.
Two straight lines intersect as shown.
 
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The measure of the angle marked <math>\boxed { }</math> is
The measure of the angle marked <math>\boxed { }</math> is



Latest revision as of 11:14, 22 April 2025

Problem

Two straight lines intersect as shown.


An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.


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