1999 CEMC Pascal Problems/Problem 6

Problem

In the diagram, $a + b$ equals

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$\text{ (A) }\ 10 \qquad\text{ (B) }\ 85 \qquad\text{ (C) }\ 110 \qquad\text{ (D) }\ 170 \qquad\text{ (E) }\ 190$

Solution

The sum of all the measures of the angles must be $360^{\circ}$ since the number of degrees in a full circle is $360^{\circ}$ . Setting up an equation using this fact, we have:

$a + b + 60 + 110 = 360$

$a + b + 170 = 360$

$a + b = 360 - 170 = \boxed {\textbf {(E) } 190}$

~anabel.disher

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1999 CEMC Pascal Problems/Problem 6

Problem

Solution