2 intersecting lines are shown. A line with points T, R, W intersects a line with points S, R, V at point R. 4 angles are created. Clockwise, from the top, the angles are blank, (3 x) degrees, blank, (x + 40) degrees.
What is the value of x?
20
35
60
70
We know that the sum of the angles around a point is 360 degrees. So, we can set up the equation:
(3x) + (x + 40) + (180) + (180) = 360
Combining like terms and simplifying, we get:
5x + 220 = 360
Subtracting 220 from both sides, we get:
5x = 140
Dividing both sides by 5, we get:
x = 28
So, the value of x is 28. None of the given answer choices are correct.
To find the value of x, we can use the fact that angles in a straight line add up to 180 degrees.
The two angles on the left side of point R add up to (3x) degrees, and the two angles on the right side of point R add up to (x + 40) degrees.
Since the lines intersect at point R, the angle on the left side of point R and the angle on the right side of point R must add up to 180 degrees.
Therefore, we have the equation:
(3x) + (x + 40) = 180
Combining like terms:
4x + 40 = 180
Subtracting 40 from both sides:
4x = 140
Dividing both sides by 4:
x = 35
Therefore, the value of x is 35.