Answer:
A) x = 6
B) ∠3 = 29°
C) ∠1 = 29°
D) ∠2 = 151°
Step-by-step explanation:
Given line e // line d and line c is transversal
Part A: If ∠3 = 5x-1 and ∠5 = 3x + 11 , find x
∠3 = ∠5 because alternate angles are congruent.
So, 5x - 1 = 3x + 11 Combine like terms
5x - 3x = 11 + 1
2x = 12
x = 6
Part B: If ∠3 = 5x-1 and ∠5 = 3x + 11 , find ∠3
∠3 = ∠5 because alternate angles are congruent.
So, 5x - 1 = 3x + 11 Combine like terms
5x - 3x = 11 + 1
2x = 12
x = 6
∴ ∠3 = 5x - 1 = 5 * 6 - 1 =30 - 1 = 29°
Part C: If ∠3 = 5x-1 and ∠5 = 3x + 11 , find ∠1
∠3 = ∠1 because vertically opposite angles are congruent
∠3 = 29°
∴∠1 = 29°
Part D: If ∠3 = 5x-1 and ∠5 = 3x + 11 , find ∠2
The angles 2 and 3 are supplementary angles.
∠3 = 29°
∠2 + ∠3 = 180°
∠2 = 180° - ∠3 = 180° - 29° = 151°
∴ ∠2 = 151°
