If angle AOB=4x+15 and angle AOC=3x+25, find the degree measured of AOB and AOC
X 34,aoc 58Degree Boc 122Degree
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To find the degree measures of angles AOB and AOC, we need to solve for x. Once we have the value of x, we can substitute it into the given expressions to find the degree measures.
Since angle AOB and angle AOC are on a straight line, they are supplementary angles, which means their sum is 180 degrees.
So, we have the equation:
AOB + AOC = 180
Now, let's substitute the given expressions into the equation:
(4x + 15) + (3x + 25) = 180
Simplify the equation:
7x + 40 = 180
Now, let's isolate x by subtracting 40 from both sides of the equation:
7x = 180 - 40
7x = 140
To solve for x, divide both sides of the equation by 7:
x = 140 / 7
x = 20
Now that we have the value of x, we can substitute it back into the expressions for angle AOB and angle AOC to find their degree measures.
For angle AOB:
Angle AOB = 4x + 15
Angle AOB = 4(20) + 15
Angle AOB = 80 + 15
Angle AOB = 95 degrees
Similarly, for angle AOC:
Angle AOC = 3x + 25
Angle AOC = 3(20) + 25
Angle AOC = 60 + 25
Angle AOC = 85 degrees
Therefore, the degree measure of angle AOB is 95 degrees, and the degree measure of angle AOC is 85 degrees.