If M<AOC = 49°, M<BOC = 2x+10. and M<AOB = 4x-15, find the degree measure of <BOC and <AOB
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°
To find the degree measure of <BOC and <AOB, we can use the fact that the sum of angles in a triangle is 180 degrees.
We are given that M<AOC = 49° and M<AOB = 4x-15.
Since the angles in a triangle add up to 180 degrees, we can write the equation:
M<AOC + M<BOC + M<AOB = 180
Substituting the given values, we get:
49 + 2x + 10 + (4x-15) = 180
Combine like terms:
6x + 44 - 15 = 180
6x + 29 = 180
Subtract 29 from both sides:
6x = 151
Divide by 6:
x = 25.1667
Now we can find the measure of <BOC and <AOB by substituting the value of x into the expressions:
M<BOC = 2x + 10 = 2(25.1667) + 10 = 60.3334 ≈ 60°
M<AOB = 4x - 15 = 4(25.1667) - 15 = 86.6668 ≈ 87°
Therefore, the correct answer is:
C- M<BOC = 28°; M<AOB=21°
To solve this problem, we need to use the Angle Sum Property and the given information.
According to the Angle Sum Property, the sum of the measures of the angles in a triangle is always 180 degrees.
Given:
M<AOC = 49°
M<BOC = 2x + 10
M<AOB = 4x - 15
We know that the sum of the angles in triangle AOC is 180 degrees. So we can write the equation:
49 + 2x + 10 + M<AOB = 180
Simplifying the equation, we get:
2x + M<AOB + 59 = 180
Now let's consider triangle BOC. This triangle also has a sum of 180 degrees. So we can write the equation:
2x + 10 + M<AOB + M<BOC = 180
Substituting the value of M<AOB from the previous equation, we get:
2x + 10 + (2x + M<AOB + 59) + M<BOC = 180
Simplifying the equation, we get:
4x + 69 + M<BOC = 180
Now let's solve for x:
4x + 69 + M<BOC = 180
Subtracting 69 from both sides, we get:
4x + M<BOC = 111
Since we know M<BOC = 2x + 10, we can substitute that in the equation:
4x + 2x + 10 = 111
Combining like terms, we get:
6x + 10 = 111
Subtracting 10 from both sides, we get:
6x = 101
Dividing by 6, we get:
x = 16.83
Now that we have the value of x, we can substitute it in the equations to find the degree measure of M<BOC and M<AOB.
M<BOC = 2x + 10 = 2(16.83) + 10 = 33.66 + 10 = 43.66°
M<AOB = 4x - 15 = 4(16.83) - 15 = 67.32 - 15 = 52.32°
Therefore, the degree measure of M<BOC is 43.66° and the degree measure of M<AOB is 52.32°.
The correct answer is option D- M<BOC = 31°; M<AOB = 18°.