One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 45 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.

Question

anonymous · Answer

$$\textrm{Let us denote the three angles of the \triangle as } \theta_1, \theta_2, \theta_3. \ \textrm{Since this is a triangle, } \theta_1 + \theta_2 + \theta_3 = 180 \
\textrm{Givens: } \theta_1 = 3\theta_2 \hspace{5em} \theta_3 = \theta_2 + 45 \
\textrm{After substitution: } 3\theta_2 + \theta_2 + \theta_2 + 45 = 180 \
\hspace{8.4em} 5\theta_2 = 135 \
\hspace{8.4em} \theta_2 = 27 \
\textrm{Since we want to find the biggest angle: } \theta_1= 3\theta_2 = 3 * 27 = 81$$