Question

Triangle ABC is shown with its exterior angles. Angle BAC is (3p - 6) degrees and angle BCA is 84 degrees. Exterior angle XBC is (p + 4) degrees. What is the measure of angle XBC?

Answer 1

The calculation for the measure of angle XBC results in a negative value, which is not possible for an angle. It implies there is an error in the given expressions or in our understanding of the problem.

Step-by-step explanation:

To find the measure of angle XBC, we will use the fact that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Given that angle BAC is (3p - 6) degrees and angle BCA is 84 degrees, we can create an equation since these are the two non-adjacent interior angles that sum up to exterior angle XBC.

Let's set up the equation:
XBC = BAC + BCA
(p + 4) = (3p - 6) + 84

Solving this equation will give us the value of p:

(p + 4) = (3p - 6) + 84
p + 4 = 3p + 78
2p = -74
p = -37

Now, substitute the value of p back into the expression for XBC:

XBC = (-37 + 4) degrees
XBC = -33 degrees

The calculation results in a negative angle, which is not possible for the measure of an angle. There must have been an error in the given expressions or in the understanding of the problem.