Rushawn lined up the interior angles of the triangle along line p below.

Question

Triangle A B C. Angles A, B, and C are shown on line p.

When the measure of angle C decreases, what happens to the measures of angles A and B on line p?
Both sections increase.
Both sections decrease.
One section increases, and the other section decreases.
What will happen to the individual sections cannot be determined, but the size of the two sections together increases.

Answer 1

In a triangle, the sum of the interior angles is always \(180^\circ\). Therefore, if the measure of angle \(C\) decreases, it means that the total of angles \(A\) and \(B\) must increase in order to keep the total sum at \(180^\circ\).

Consequently, when angle \(C\) decreases:

• The measures of angles \(A\) and \(B\) together must increase.
• This means at least one of the angles \(A\) or \(B\) must increase to compensate for the decrease in angle \(C\).

Thus, the correct answer is: One section increases, and the other section decreases. This is because if one angle increases while the other angle remains constant (or both increase), then the total still balances with the decrease in angle \(C\).