2012 CEMC Gauss (Grade 8) Problems/Problem 4

Problem

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

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