Question

Triangle A B C is shown with its exterior angles. Angle B A C is (p + 4) degrees and angle A C B is 84 degrees. Exterior angle X B C is (3 p minus 6 degrees).
What is the measure of ∠XBC?

m∠XBC = m∠BAC + m∠BCA
3p – 6 = p + 4 + 84
3p – 6 = p + 88
2p – 6 = 88
2p = 94

Answer 1

Answer:

The diagram of the question is attached here.

The measure of $\angle XBC=135\ (deg)$

Step-by-step explanation:

All the options given here will be used to find the numeric value of $\angle XBC$

Here it is shown systematically.

Exterior angle theorem: Sum of two interior angles are equal to the measure of opposite exterior angle in a triangle.

To find $\angle XBC$

$m\angle XBC = m\angle BAC + m\angle BCA$

Plugging the values.

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

$3p-6 = p + 88$

Subtracting $p$ both sides.

$2p-6 = 88$

$2p = 94$

Dividing $2$ both sides.

$p=\frac{94}{2}=47$

So plugging the value of $p=47$ in $3p-6$ we will get the measure of $\angle XBC$.

So $\angle XBC=(3p-6)=3(47)-6=135\ (deg)$

The measure of $\angle XBC$ is $135\ degrees$.