Answer:
x = 50
Explanation:
Given that the two vertical lines are parallel, and they are being cut by a transversal. We are also given two angle measures (x + 10) and (2x + 20). From the diagram, we can tell that both angles are on the same side of the transversal and are inside the parallel lines. To determine the value of x, we will have to apply some exterior/interior/180° angle properties.
Requirements for each method (exterior/interior/180°):
- Equate the angles using an equation ⇒ Only possible if both angles satisfy an Interior/Exterior angle property.
- Compare the sum of two angles with 180° ⇒ If (1) both angles are on the same side of the transversal and (2) are inside the parallel lines.
Here, both angles are on the same side of the transversal and are inside the parallel lines. Therefore, we will apply the second method to solve.
The sum of the two angles is (x + 10)° + (2x + 20)°. Let us now compare the sum of the two angles with 180° as they are supplementary (180°).
- ⇒ (x + 10)° + (2x + 20)° = 180
To simplify, we must open the parentheses to combine like terms
- ⇒ x + 10 + 2x + 20 = 180
- ⇒ 3x + 30 = 180
Isolate the variable completely. This can be done by removing the coefficient (multiplying/dividing on both sides if needed) and the terms that are being added/subtracted (adding/subtracting on both sides) to it.
- ⇒ 3x + 30 - 30 = 180 - 30
- ⇒ 3x = 180 - 30 = 150
- ⇒ 3x/3 = x = 150/3 = 50
Therefore, the value of x is 50.