A triangle has an angle that measures 110°. The other two angles are in a ratio of 3:4. What are the measures of those two angles?

answer:

when they are equal, y=y, so we can say:

x^2+5x-2=x+1   subtract x from both sides

x^2+4x-2=1   add 2 to both sides

x^2+4x=3, now add half the linear coefficient squared, (4/2)^2=4

x^2+4x+4=3+4 now the left side is a perfect square

(x+2)^2=7   now take the square root of both sides

x+2=±√7   subtract 2 from both sides

x=-2±√7

x=-2+√7 and -2-√7

y=x+1 the two points where these equations are equal are:

(-2-√7, -1-√7) and (-2+√7, -1+√7)

or approximately:

(-4.65, -3.65) and (0.65, 1.65)