Question

What is the measure of ∠XBC?

1. m∠XBC = m∠BAC + m∠BCA

2. 3p – 6 = p + 4 + 84

3. 3p – 6 = p + 88

4. 2p – 6 = 88

5. 2p = 94

m∠XBC =

Answer 1

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 the case of this question this fact sounds as

m∠XBC = m∠BAC + m∠BCA (option 1).

Now if

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

then

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°.

Answer: m∠XBC=135°.

Answer 2

we Know that
m∠ABC=180-[(p+4)+84]--------> 180-[p+88]=92-p
m∠ABC=(92-p)° equation 1
and
m∠ABC+(3p-6)=180----------m∠ABC=180+6-3p
m∠ABC=186-3p equation 2
(1)=(2)
(92-p)=186-3p-----------> 186-92=-p+3p--------------> 2p=94

p=47°
therefore
m∠XBC=(3p-6)°---------->(3*47-6)=135°

the answer is
m∠XBC=135°