The values of A and B are 105° and 50°
Step-by-step explanation:
We can find A by using lines [tex]l_{1}[/tex] , [tex]l_{2}[/tex] and line n
∵ [tex]l_{1}[/tex] // [tex]l_{2}[/tex]
∵ n is a transversal
∴ Angle A is congruent to the supplement angle of 75° ⇒
corresponding angles
∵ The sum of measures of the supplement angles is 180°
∴ A + 75 = 180
- Subtract 75 from both sides
∴ A = 105°
By using lines [tex]l_{1}[/tex] , [tex]l_{2}[/tex] and line m we can find B
∵ [tex]l_{1}[/tex] // [tex]l_{2}[/tex]
∵ m is a transversal
∴ Angle 55° is congruent to the angle between [tex]l_{2}[/tex] and m
above 75° ⇒ alternate angles
∴ The measure of this angle is 55°
∵ This angle , 75° and B formed a line
∴ The sum of their measures is 180°
∴ 55° + 75° + B = 180°
- Add like terms in the left hand side
∴ 130 + B = 180
- Subtract 130 from both sides
∴ B = 50°
The values of A and B are 105° and 50°
Learn more:
You can learn more about parallel lines in brainly.com/question/10483199
#LearnwithBrainly
