2024 CEMC Gauss (Grade 8) Problems/Problem 8

Problem

In the diagram, $\angle ABC$ is a straight angle.

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The value of $x$ is

$\textbf{(A)}\ 80 \qquad\textbf{(B)}\ 65 \qquad\textbf{(C)}\ 75 \qquad\textbf{(D)}\ 70 \qquad\textbf{(E)}\ 60$

Since $\angle ABC$ is a straight angle, we know that the sum of the three angles is $180^{\circ}$ . Thus, we have:

$40^{\circ} + x^{\circ} + x^{\circ} = 180^{\circ}$

Combining like terms on the left side of the equation, we get:

$40^{\circ} + 2x^{\circ} = 180^{\circ}$

Subtracting $40^{\circ}$ from both sides we have:

$2x^{\circ} = 140^{\circ}$

This gives:

$x = \boxed {\textbf {(D) } 70}$

~anabel.disher