Question 211837
One angle of a triangle is 3 less than twice another.  The other is 4X the sum of the small angle and 2.  What are the angle measurements??


Let the smallest angle be S


Since the middle angle is 3 less than twice the smallest, then middle angle = 2S - 3


Since the largest angle is 4 times the sum of the smallest angle, and 2, then largest angle = 4(S + 2), or 4S + 8


Since the angles of a triangle are supplementary, it follows that:


S + 2S - 3 + 4S + 8 = 180


7S + 5 = 180


7S = 175


{{{S = 175/7}}} = 25


Middle angle = 47 ------> [2(25) - 3]


Largest angle = 108 -----> [4(25 + 2)]


Therefore, the smallest, middle, and largest angles are: {{{highlight_green(25_47_and_108)}}}, respectively.