2. Parallel lines rand s are cut by two transversals, parallel lines tand u.

Which angles are alternate interior angles with angle 3?
C 25 and 213
C 27 and 215
26 and 216
28 and 214

Option A: ∠5 and ∠13 are alternate interior angles with angle 3.

Solution:

To find which angles are alternate interior angles with angle 3:

Option A: ∠5 and ∠13

If t and u are parallels, then r is a transversal.

3 and 13 are alternate interior angles.

If r and s are parallels, then t is a transversal.

3 and 5 are alternate interior angles.

Therefore ∠5 and ∠13 are alternate interior angles with angle 3.

Hence it is true.

Option B: ∠7 and ∠15

∠7 is a corresponding angle of ∠3 on the same side of the transversal.

∠15 is a corresponding angle of ∠3 on the same side of the transversal.

So, ∠7 and ∠15 are not alternate interior angles with angle 3.

Hence it is not true.

Option C: ∠6 and ∠16

∠6 is an alternate exterior angle of ∠3.

∠16 is an alternate exterior angle of ∠3.

So, ∠6 and ∠16 are not alternate interior angles with angle 3.

Hence it is not true.

Option D: ∠8 and ∠14

∠8 is an interior angle on the same side.

∠14 is an interior angle on the same side.

So, ∠8 and ∠14 are not alternate interior angles with angle 3.

Hence it is not true.

Therefore ∠5 and ∠13 are alternate interior angles with angle 3.

Option A is the correct answer.

goog may have it for you

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.