Question

in △ABC the measure of angle A is 2x + 3, the measure of angle B is 4x + 2, and the measure of angle C is 2x - 1. what are the measures of the angles?

Answer 1

All angles in a triangle add to 180. So, we must add all those expressions together and set them equal to 180.

2x+3+4x+2+2x-1=180
Now we combine like terms (2x+4x+3x is 8x, 3+2-1 is 4)
8x+4=180
Now subtract 4 from both sides (4-4 is 0, 180-4 is 176)
8x=176
Now divide both sides by 8.
x=22.

Now substitute 22 wherever you see x in each expression.

2x+3 = 2(22)+3 = 44+ 3 = 47
4x+2 = 4(22)+2 = 88+2 = 90
2x-1 = 2(22)-1 = 44-1 = 43

So the final answer is A=47°, B=90°, C=43°

To check, add these numbers together and see if they equal 180.

90+43+47 is 180, so the answers are correct.