Question

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:

From geometrical theorem it is concluded that ‘The measure of an exterior angle of triangle is equal to the sum of measures of two interior angles of triangle that are not supplementary with this exterior angles’.

In this case as shown in the drawing , this question this fact case will be  as given below :-

m∠XBC = m∠BAC + m∠BCA,

Now if : m∠XBC=(3p-6)°: m∠BAC=(p+4)°: m∠BCA=84°,

then we get the equation :

3p-6=p+4+84

(option 2), 3p-6=p+88

(option 3), 3p-p-6=p-p+88,2p-6=88

(option 4), 2p-6+6=88+6,2p=94

(option 5), p=47.

Then m∠XBC=(3p-6)°=(3·47-6)°=135°.

Therefore, Answer: m∠XBC=135°.

Answer 2

Answer: 135°

                 

Explanation: