Answer:
Part A) [tex]x=6[/tex]
Part B) ∠3=29°
Part C) ∠1=29°
Part D) ∠2=151°
Step-by-step explanation:
Part A) If ∠3=5x-1 and ∠5=3x+11, then x=?
we know that
∠3=∠5 ----> by alternate interior angles
so
substitute and solve for x
[tex]5x-1=3x+11[/tex]
[tex]5x-3x=11+1[/tex]
[tex]2x=12[/tex]
[tex]x=6[/tex]
Part B) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠3=?
we know that
∠3=5x-1
The value of x is
[tex]x=6[/tex]
substitute
∠3=5(6)-1=29°
Part C) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠1=?
we know that
∠1=∠3 ----> by vertical angles
we have
∠3=29°
therefore
∠1=29°
Part D) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠2=?
we know that
∠1+∠2=180° ----> by supplementary angles
we have
∠1=29°
substitute
29°+∠2=180°
∠2=180°-29°
∠2=151°
