Answer:
x = 20; the labeled angles are 80° and 100° ⇒ the last answer
Step-by-step explanation:
* Lets revise some facts about a parallelism
- If two lines are parallel, and intersected by a line, there are 3
pair of angles are formed
1) Alternate angles equal in measures (corners of Z letter)
2) Corresponding angles equal in measure (corners in F letter)
3) Interior supplementary angles their sum is 180° (corners of U letter)
* Now lets solve the problem
∵ There are two parallel lines intersect by another line
- The formed U letter
∴ The labeled angles are interior supplementary angles
∴ Their sum = 180°
∴ 5x + 4x = 180° ⇒ add the like terms
∴ 9x = 180° ⇒ divide both sides by 9
∴ x = 20°
* Lets find the measure of the labeled angles
∵ The measure of one of them is 4x°
∴ Its measure = 4(20) = 80°
∵ The measure of the other is 5x°
∴ Its measure = 5(20) = 100°
