Hi there!
We can start off by taking out some key information from this problem.
- 6 flowers in the vase.
- 3 are roses. (3/6)
- 2 are peonies. (2/6)
- 1 is a Lily. (1/6)
By converting all of the flowers to have a common denominator we can clearly see that 1/6 of the flowers are lilies.
<h3>
Answer: 226 degrees</h3>
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Explanation:
Notice the tickmarks on the segments in the diagram. This tells us that chords DC and CB are the same distance from the center. It furthermore means that DC and CB are the same length, and arcs DC and CB are the same measure
arc DC = arc CB
12x+7 = 18x-23
12x-18x = -23-7
-6x = -30
x = -30/(-6)
x = 5
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Use this x value to find the measure of arcs DC and CB
- arc DC = 12x+7 = 12*5+7 = 67
- arc CB = 18x-23 = 18*5-23 = 67
We get the same measure for each, which helps confirm we have the correct x value.
The two arcs in question add to 67+67 = 134 degrees. This is the measure of arc DCB. Subtract this from 360 to get the answer
arc DAB = 360-(arc DCB) = 360-134 = 226 degrees
I'm using the idea that (arc DCB) + (arc DAB) = 360 since the two arcs form a full circle.
You would start by finding the area of the circle and then finding the area of the rectangle. After finding both, subtract the area of the rectangle from that of the circle. <span />
2:3:5
2x+3x+5x=180
10x=180
x=18
2x=36
3x=54
5x=90
