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
From the given information, we have:
m<AOC = 49 degrees
m<BOC = 2x + 10
m<AOB = 4x - 15
Since the sum of the angles in a triangle is 180 degrees, we can set up the following equation:
m<AOC + m<BOC + m<AOB = 180
Substituting the given angle measures:
49 + (2x + 10) + (4x - 15) = 180
Simplifying this equation gives:
6x + 44 = 180
Subtracting 44 from both sides:
6x = 136
Dividing both sides by 6:
x = 22.67
Now we can find the measure of <BOC and <AOB using the values of x:
m<BOC = 2(22.67) + 10 = 45.34 + 10 = 55.34 degrees
m<AOB = 4(22.67) - 15 = 90.68 - 15 = 75.68 degrees
Therefore, the degree measure of <BOC is 55.34 degrees, and the degree measure of <AOB is 75.68 degrees.
The correct answer is none of the provided options.
To find the degree measure of ∠BOC and ∠AOB, we can set up and solve two equations.
Given:
m∠AOC = 49 degrees
m∠BOC = 2x + 10
m∠AOB = 4x - 15
To find the degree measure of ∠BOC, we'll equate it to 49 degrees:
2x + 10 = 49
Subtracting 10 from both sides:
2x = 39
Dividing both sides by 2:
x = 19.5
Now, we can substitute the value of x back into the equation for ∠BOC to find its degree measure:
m∠BOC = 2(19.5) + 10
m∠BOC = 39 + 10
m∠BOC = 49 degrees
Therefore, the degree measure of ∠BOC is 49 degrees.
Similarly, we can find the degree measure of ∠AOB:
m∠AOB = 4x - 15
m∠AOB = 4(19.5) - 15
m∠AOB = 78 - 15
m∠AOB = 63 degrees
Therefore, the degree measure of ∠AOB is 63 degrees.
Therefore, the correct answer is C -> m∠BOC = 28 degrees and m∠AOB = 21 degrees.