Segment addition postulate
Substitution
Distribution Property of Equality
Simplification, or Adding like terms
Subtraction property
Division Property
<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.
If you multiply or divide by a positive number the inequality sign DOES NOT CHANGE!
If you multiply or divide by a negative number the inequality sign flips around and becomes the opposite.
Think of numbers that when they are divided by 10, the remainder is 9.
So numbers like: 19, 29, 39, 49, 59, 69, 79, 89, and 99.
Now numbers that when they are divided by 9, the remainder is 8.
So numbers like: 17, 26, 35, 44, 53, 62, 71, 80, 89, and 98.
Now the number that is alike from the two sets of numbers is n.
n=89
Double check your work.
Divide 89 by 10. Remainder of 9
Divide 89 by 9. Remainder of 8.
Hope this helps :)
Twelve and one hundred sixty-five thousandths
