Find the measures of the three angles of a triangle if the largest is 4 $^ { \circ }$ smaller than 18 times the smallest and the other angle is 64 $^ { \circ }$ larger than the smallest.
A) 194 $^ { \circ }$ , 70 $^ { \circ }$ , 6 $^ { \circ }$
B) 14 $^ { \circ }$ , 115 $^ { \circ }$ , 6 $^ { \circ }$
C) 104 $^ { \circ }$ , 70 $^ { \circ }$ , 96 $^ { \circ }$
D) 104 $^ { \circ }$ , 70 $^ { \circ }$ , 6 $^ { \circ }$
E) 104 $^ { \circ }$ , 250 $^ { \circ }$ , 6 $^ { \circ }$

Question

Quizplus · Accepted Answer

Let the smallest angle be $x$. The largest angle is $18x - 4$, and the other angle is $x + 64$. The sum of angles in a triangle is $180^\circ$, so $x + (18x - 4) + (x + 64) = 180$, which simplifies to $20x + 60 = 180$, leading to $20x = 120$, and $x = 6^\circ$. Thus, the angles are $6^\circ$, $104^\circ$ (since $18*6 - 4 = 104$), and $70^\circ$ (since $6 + 64 = 70$).

Find the Measures of the Three Angles of a Triangle ∘^ { \circ }∘

Find the Measures of the Three Angles of a Triangle $^ { \circ }$