The second angle of a triangle is 4 times as large as the first. The third angle is $140^{\circ}$ more than the sum of the other two angles. Find the measure of the second angle.
A) $20^{\circ}$
B) $1^{\circ}$
C) $16^{\circ}$
D) $4^{\circ}$

Question

Quizplus · Accepted Answer

The sum of angles in a triangle is $180^{\circ}$. Let the first angle be $x$, so the second angle is $4x$, and the third angle is $140^{\circ} + x + 4x = 140^{\circ} + 5x$. The equation is $x + 4x + 140^{\circ} + 5x = 180^{\circ}$, simplifying to $10x = 40^{\circ}$, so $x = 4^{\circ}$ and the second angle $4x = 16^{\circ}$.

The Second Angle of a Triangle Is 4 Times as Large