26.1k views
1 vote
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 =

What is the measure of ∠XBC? 1. m∠XBC = m∠BAC + m∠BCA 2. 3p – 6 = p + 4 + 84 3. 3p-example-1
User Slavugan
by
9.1k points

2 Answers

4 votes

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°.

User Azat Nugusbayev
by
7.8k points
5 votes
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°
User LeonH
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories