Question

If the measure of angle 5 is (11x-14) and x=6, which expression could represent the measure of angle 2?

Answer choices:

(8x+4)
(9x+2)
(20x+8)
(18x+20)

Answer 1

For this case we have that angle 5 is opposite by the vertex to angle 2, therefore they are equal.

We have that angle 5 measures
`11x-14`. We have
`x = 6,` so angle 5 measures
`11 (6) -14 = 66-14 = 52`

Therefore, angle 2 should measure 52.

We test the options, taking into account that
`x = 6.`

Option A:

`8x + 4\\8 (6) + 4 = 48 + 4 = 52`

Thus, the correct option is A.

Answer:

Option A

Answer 2

(8x+4)

Explanation:

we know that

m∠5=m∠2 -----> by vertical angles

we have

m∠5=(11x-14)

substitute the value of x

x=6

m∠5=11(6)-14=52°

therefore

m∠2=52°

Verify the choices

1) (8x+4)=8(6)+4=52° -----> The expression could represent the measure of angle 2

2) (9x+2)=9(6)+4=58° -----> The expression not represent the measure of angle 2

3) (20x+8)=20(6)+8=128° -----> The expression not represent the measure of angle 2

2) (18x+20)=18(6)+20=128° -----> The expression not represent the measure of angle 2