Question

A.) If angle 3 = 5x-1 and angle 5-3x+11, then x= B.) If angle 3 = 5x-1, and angle 5 = 3x + 11, then the measure of angle 3= C.) If 23 = 5x-1, and 25 = 3x+ 11, then the measure of angle 1= D.) If angle 3 = 5x-1, and angle 5 = 3x + 11, then the measure of angle 2 =

Answer 1

1) Gathering the data

∠3 = 5x -1

∠5=3x +11

∠3=?

2) The angles ∠3 and ∠5 are alternate interior angles, therefore they are congruent ones. So we can write:

5x -1 = 3x +11

5x -3x = 11 +1

2x = 12

x = 6

The measure of angle m∠3 =

5(6) -1

30-1

29º As ∠5 is also congruent then m∠5= 29º

3) ∠1 According to the Vertical Angle Theorem has the same measure as the ∠3, So we can say that ∠1 = 29º

∠2 is supplementary to ∠1

m∠2=180 -29

m∠2=151º