Question

PLEASE HELP WILL FAN AND MEDAL In ΔABC the measure of ∠A is 2x + 3, the measure of ∠B is 4x + 2, and the measure of ∠C is 2x - 1. What are the measures of the angles?

Answer 1

All angles of a triangle sum up to 180 degrees. Knowing this, you just need to add up all expressions together and set them equal to 180. Then, solve for your x-value.

Answer 2

After that, plug your x-value into each equation to get your corresponding angles. Good luck!

Answer 3

\[2x + 3 + \left( 4x + 2 \right) + \left( 2x - 1 \right) = 180\]\[x = ~?\]

Answer 4

@Cardinal_Carlo I got x = 21.75. Is that correct?

Answer 5

Close. You should've gotten x = 22.

Answer 6

@Cardinal_Carlo Can you show me how you got 22?

Answer 7

\[2x+3+(4x+2)+(2x−1)=180\]\[8x + 4 = 180\]\[8x = 180 - 4 = 176\]\[x = \frac{ 176 }{ 8 } = 22\]

Answer 8

Now, you just have to plug this x-value into all three equations above to get angles A-C.

Answer 9

@Cardinal_Carlo Thanks, I understand it now. I put the wrong integer in ∠C. :)

Answer 10

Well, you've caught your mistake, and that's awesome.

Answer 11

@Cardinal_Carlo Thanks, I got the angle values as ∠A = 47 ∠B = 100 ∠C = 43, but when I added them, I got 190. Did I do something wrong?

Answer 12

Yes, angle B should be 90.

Answer 13

@Cardinal_Carlo Oh, sorry. I didn't realize I added wrong. :)

Answer 14

That's okay. At least, you caught yourself.

Answer 15

^_^