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?

1) m∠xbc = m∠bac
2) m∠xbc = m∠bca
3) 3p - 6 = p + 4
4) 84
5) 3p - 6 = 88
6) 2p - 6 = 88
7) 2p = 94

Answer 1

To find the measure of exterior angle XBC, the value of 'p' is determined using the given expressions for the interior angles and the exterior angle property. Solving the equation 2p - 6 = 88 gives p = 47, and substituting 'p' back into the expression for XBC gives a measure of 51 degrees.

Step-by-step explanation:

The question involves finding the measure of exterior angle XBC of a triangle given the measures of the interior angles in terms of a variable 'p'. Since exterior angle XBC is equal to the sum of the two non-adjacent interior angles, we set up an equation to find the value of 'p' and thus the measure of angle XBC.

Let's denote the measure of angle BAC as 'A', angle BCA as 'C', and exterior angle XBC as 'XBC'. Given that:

• A = (3p - 6)°
• C = 84°
• XBC = (p + 4)°

By the exterior angle property, we have:

XBC = A + C

Substituting the given values, we get:

(p + 4) = (3p - 6) + 84

To find 'p', we solve the equation:

2p - 6 = 88

2p = 94

p = 47

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

XBC = (47 + 4)°

XBC = 51°

Therefore, the measure of exterior angle XBC is 51 degrees.