SOLUTION: The second angle of a triangle is 4 times as large as the first. The third angle is 45 degrees less than the sum of the other two angles. Find the measurment of each angle.

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Question 147624: The second angle of a triangle is 4 times as large as the first. The third angle is 45 degrees less than the sum of the other two angles. Find the measurment of each angle.
Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
First set up an equation. The sums of the angles of a triangle is 180 degrees. So set the equation equal to that. Assign a value for each of the angles. Let one of them (the first one) be x. Then the second one would be 4x, and the third would be x+4x-45. Since the second angle of the triangle is 4 times as large as the first and the third angle is 45 degrees less than the sum of the other two angles. This is what the word problem looks like as an equation: x%2B4x%2Bx%2B4x-45=180. Then combine like terms and get 10x-45=180. Then add 45 to both sides and get 10x=225. Divide by ten and get x=22.5. That is the measure of the smallest angle. Then simply plug 22.5 back in for x on the others. 4x=4(22.5)=90. So the second angle is 90. and the third angle is x+4x-45 or 22.5+90-45. So the third angle comes out as 67.5. Wanna check? Plug in the values for the angles in the original equation. Does 22.5+67.5+90 equal 180? Yep! So your angles are 22.5,67.5, and 90 degrees.