Solution:
Given A || B.
Vertically opposite angles are congruent.
⇒ 3x + 19 = 5x – 29
Subtract 19 on both sides.
⇒ 3x = 5x – 48
⇒ –2x = – 48
Divide by –2 on both sides.
⇒ x = 24
Sum of the adjacent angles in a straight line = 180°
m∠7 + 5x – 29 = 180°
m∠7 + 5(24) = 209°
m∠7 + 120 = 209°
m∠7 = 89°
m∠7 and m∠8 are vertically opposite angles.
m∠7 = m∠8
m∠8 = 89°
Substitute x = 24 in 3x + 7.
3x + 7 = 3(24) + 7 = 79°
∠1 and 3x + 7 are supplementary.
m∠1 + 3x + 7 = 180°
m∠1 + 79° = 180°
m∠1 = 101°
∠1 and ∠3 are vertical angles.
∠1 = ∠3
m∠3 = 101°
3x + 7 and ∠2 are vertical angles.
∠2 = 3x + 7
m∠2 = 79°
∠2 and ∠5 are alternative interior angles.
If two lines are parallel then alternative interior angles are congruent.
m∠5 = m∠2
m∠5 = 79°
∠3 and ∠4 are alternative interior angles.
m∠4 = m∠3
m∠4 = 101°
∠5 and ∠6 are vertical angles.
m∠5 = m∠6
m∠6 = 79°
Hence the value of x is 24.
The measure of ∠1 is 101°.
The measure of ∠2 is 79°.
The measure of ∠3 is 101°.
The measure of ∠4 is 101°.
The measure of ∠5 is 79°.
The measure of ∠6 is 79°.
The measure of ∠7 is 89°.
The measure of ∠8 is 89°.
