if m<AOC = 49 degress, m<BOC = 2x+10, and m<AOB = 4x-15, find the degree measure of <BOC and <AOB. The diagram is not to scale
A-> m<BOC= 21 ; m<AOB = 28
B-> m<BOC= 18; m<AOB = 31
C-> m<BOC= 28; m<AOB = 21
D-> m<BOC = 31; m<AOB = 18
We are given that m<AOC = 49 degrees. Since AOC, BOC, and AOB form a straight line, we know that the sum of their degree measures is 180 degrees.
Therefore, m<BOC + m<AOB + m<AOC = 180 degrees.
Substituting the given values, we get:
(2x+10) + (4x-15) + 49 = 180.
Simplifying the equation, we get:
6x + 44 = 180.
Subtracting 44 from both sides, we get:
6x = 136.
Dividing both sides by 6, we get:
x = 22.6667.
To find m<BOC, we substitute the value of x into m<BOC = 2x + 10:
m<BOC = 2(22.6667) + 10 = 56.3333.
To find m<AOB, we substitute the value of x into m<AOB = 4x - 15:
m<AOB = 4(22.6667) - 15 = 79.6667.
Therefore, the degree measure of <BOC is approximately 56.3333 degrees, and the degree measure of <AOB is approximately 79.6667 degrees.
None of the given answer choices match the calculated values.
To find the degree measures of <BOC and <AOB, we can set up an equation based on the given information.
Given:
m<AOC = 49 degrees
m<BOC = 2x + 10
m<AOB = 4x - 15
We know that the sum of the angles in a triangle is 180 degrees. So, we can set up the equation:
m<AOC + m<BOC + m<AOB = 180
Substituting the given values:
49 + 2x + 10 + 4x - 15 = 180
Combining like terms:
6x + 44 = 180
Subtracting 44 from both sides:
6x = 136
Dividing both sides by 6:
x = 22.67
Now we can substitute this value of x into the expressions for m<BOC and m<AOB:
m<BOC = 2(22.67) + 10 = 45.34 + 10 = 55.34
m<AOB = 4(22.67) - 15 = 90.68 - 15 = 75.68
So, the degree measures of <BOC and <AOB are approximately 55.34 and 75.68 degrees, respectively.