Difference between revisions of "2012 CEMC Gauss (Grade 8) Problems/Problem 4"

Latest revision as of 12:20, 22 April 2025

Points $P$ , $Q$ , and $R$ lie in a straight line.

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The value of $x$ is

$\text{ (A) }\ 69\qquad\text{ (B) }\ 138\qquad\text{ (C) }\ 75\qquad\text{ (D) }\ 64\qquad\text{ (E) }\ 54$

Since $\overline{PQR}$ is a straight line, it forms an angle of $180^{\circ}$ .

This means that we have the equation:

$42^{\circ} + x^{\circ} + x^{\circ} = 180^{\circ}$

$2x^{\circ} = 138^{\circ}$

$x^{\circ} = 69^{\circ}$

Thus, $x = \boxed{\textbf{(A) } 69}$

~anabel.disher

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 ==Problem==
 Points <math>P</math>, <math>Q</math>, and <math>R</math> lie in a straight line.
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 The value of <math>x</math> is