Question triangle ABC, the exterior angle of C (BCD) measure is 3X^2+8X-1. Angle A measure is 2X^2+7 Measure of angle B is 3X-2, angle C is not given. What is the value of X, measure of angle A, B, C, and BCD? and plz list all the steps for solving X.
Answer By the exterior, do you mean the the supplement of that angle?
That would mean the angle C was 180 - 3X² - 8X + 1 = 181 - 3X² - 8X.
The measure of angle A is 2X² + 7 and angle B is 3X-2, so add on C and get 180 degrees.
Since A+B+C = (2X²+7) + (3x-2) + (181 - 3X² - 8X) = 180,
like terms can be grouped together, giving 2X² - 3X² + 3x - 8X + 7 - 2 + 181 = 180.
Adding them gives -X² - 5X + 186 = 180.
Subtracting 180 from both sides gives X² + 5X - 6 = 0.
Factoring gets (X+6)(X-1) = 0.
Solving gets X+6 = 0 or X-1 = 0.
The results are X=-6 and X=1.
Angles have positive size, so take X=1.
Put that back in the formulas for A, B, and C, and you will get the answer.
A = 2X²+7 = 2+7 = 9, B = 3x-2 = 3-2 = 1, C = 181-3X²-8X = 181-3-8 = 172.
I'm not sure that is right, so what is meant by the exterior angle if not the supplement?
If it is not the supplement, put in whatever it is.
If the exterior is the complement, put in 90 instead of 180.
If the exterior is the part of the angle that is not in the triangle, put in 360 instead of 180.
If you still need help, send back another question.
