2000 CEMC Gauss (Grade 8) Problems/Problem 6

Problem

In the given diagram, what is the value of $x$ ?

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$\text{ (A) }\ 20 \qquad\text{ (B) }\ 80 \qquad\text{ (C) }\ 100 \qquad\text{ (D) }\ 120 \qquad\text{ (E) }\ 60$

Solution

Using the fact that the sum of the angles of a right triangle is $180^{\circ}$ , the unlabeled angle in the triangle must be equal to $180 - 40 - x = 140 - x$

Since $60^{\circ}$ and $140 - x$ are vertical angles, they are equal to each other, giving us:

$140 - x = 60$

$x + 60 = 140$

$x = \boxed {\textbf {(B) } 80}$

~anabel.disher

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2000 CEMC Gauss (Grade 8) Problems/Problem 6

Problem

Solution