if m∠BAC = (7x +1)° and the m∠BCA = (5x +9)°, then what is the measure of the vertex angle?

Answer 1

I think that we are missing a little information here. Is ΔABC isosceles maybe? If you were also told that the triangle is isosceles and that ∠BAC and ∠BCA are the base angles, then we can set m∠BAC = m∠BCA and solve:

7x + 1 = 5x + 9 subtract 5x from both sides

2x + 1 = 9 subtract 1 from both sides

2x = 8 divide by 2

x = 4

Plugging back into the expressions for the angle measurements:

7(4) + 1 = 29 and also 5(4) + 9 = 29ºº

Now we can find the vertex angle by subtracting from 180º. 180 - 29 - 29 = 122º.

Like I said before, this only works if the assumptions I made about the problem are true.