A circle is divided into four segments from the center of the circle. One segment is x degree and each of the other three segments increases by 20 degree from the previous segment. What is the value of the largest segment?
a. 60 degree
b. 80 degree
c. 100 degree
d. 120 degree
e. 140 degree
please answer and explain
x+(x+20)+(x+40)+(x+60) = 360
so, what is x+60?
50+60=110
50+60 = 110, but where do you get the 50?
To find the value of the largest segment, we need to determine the angle measure of each of the segments.
Let's start with the given information: one segment is x degrees, and each of the other three segments increases by 20 degrees from the previous segment.
We can write the angles of the segments as follows:
Segment 1: x degrees
Segment 2: x + 20 degrees
Segment 3: x + 20 + 20 degrees = x + 40 degrees
Segment 4: x + 20 + 20 + 20 degrees = x + 60 degrees
Now we know the angle measures of all four segments in terms of x.
Since the circle is divided into four segments, the sum of all the segments should add up to 360 degrees. Therefore, we can set up an equation:
x + (x + 20) + (x + 40) + (x + 60) = 360
Simplifying the equation:
4x + 120 = 360
4x = 240
x = 60
Now we can substitute the value of x back into the expressions for each segment:
Segment 1: x degrees = 60 degrees
Segment 2: x + 20 degrees = 60 + 20 = 80 degrees
Segment 3: x + 40 degrees = 60 + 40 = 100 degrees
Segment 4: x + 60 degrees = 60 + 60 = 120 degrees
Therefore, the value of the largest segment is 120 degrees, which corresponds to option (d).