if m<AOC = 85 degrees, m<BOC = 2x+10, and m<AOB = 4x-15, find the degree measure of <BOC and <AOB. The diagram is not to scale
I apologize for the incorrect response. Let's try to solve it again.
We are given:
m<AOC = 85 degrees
m<BOC = 2x + 10
m<AOB = 4x - 15
To find the degree measure of <BOC and <AOB, we need to find the value of x first.
Using the angle sum property in triangle AOC, we have:
m<AOC + m<BOC + m<BOA = 180 degrees
Substituting the given values, we have:
85 + (2x + 10) + (4x - 15) = 180
Combine like terms:
6x + 80 = 180
Subtract 80 from both sides:
6x = 100
Divide both sides by 6:
x = 100/6
x = 16.67
Now we can substitute this value of x back into the expressions for m<BOC and m<AOB:
m<BOC = 2(16.67) + 10 = 43.34 degrees
m<AOB = 4(16.67) - 15 = 46.68 degrees
So, the degree measure of <BOC is 43.34 degrees and the degree measure of <AOB is 46.68 degrees.
Since we know that the sum of angles in a triangle is 180 degrees, we can write the equation:
85 + 2x + 10 + 4x - 15 = 180
Combine like terms:
6x + 80 = 180
Subtract 80 from both sides:
6x = 100
Divide both sides by 6:
x = 16.67
Now we can substitute this value of x back into the expressions for m<BOC and m<AOB:
m<BOC = 2(16.67) + 10 = 43.34 degrees
m<AOB = 4(16.67) - 15 = 46.68 degrees
So, the degree measure of <BOC is 43.34 degrees, and the degree measure of <AOB is 46.68 degrees.
thats not it
To find the degree measures of ∠BOC and ∠AOB, we can use the fact that the sum of angles around a point is 360 degrees.
Step 1: Find the value of x
Since ∠AOC and ∠BOC are adjacent angles, we can use the property that adjacent angles are supplementary, which means their angle measures add up to 180 degrees.
Therefore, ∠AOC + ∠BOC = 180 degrees.
Given:
m<AOC = 85 degrees
m<BOC = 2x + 10
Replacing the given values, we get:
85 + (2x + 10) = 180
Step 2: Solve for x
Simplify the equation:
2x + 95 = 180
Subtract 95 from both sides:
2x = 180 - 95
2x = 85
Divide both sides by 2:
x = 85 / 2
x = 42.5
Step 3: Find the degree measures of ∠BOC and ∠AOB
Given:
m<AOB = 4x - 15
Replace x with the value we found in step 2:
m<AOB = 4(42.5) - 15
m<AOB = 170 - 15
m<AOB = 155 degrees
m<BOC = 2x + 10
m<BOC = 2(42.5) + 10
m<BOC = 85 + 10
m<BOC = 95 degrees
Therefore, the degree measure of ∠BOC is 95 degrees and the degree measure of ∠AOB is 155 degrees.
To find the degree measure of ∠BOC and ∠AOB, we need to use the given information and apply some properties of angles.
From the information given, we know that:
- ∠AOC = 85 degrees (m<AOC = 85 degrees)
- ∠BOC = 2x + 10
- ∠AOB = 4x - 15
To find the measure of the angles, we need to set up an equation using the angle sum property. In a triangle, the sum of the three angles is always equal to 180 degrees.
So we can write the equation as:
∠AOC + ∠BOC + ∠AOB = 180 degrees
Substituting the given values, we have:
85 + (2x + 10) + (4x - 15) = 180
Now, let's solve the equation for x:
85 + 2x + 10 + 4x - 15 = 180
Combine like terms:
6x + 80 = 180
Subtract 80 from both sides of the equation:
6x = 100
Divide both sides of the equation by 6:
x = 16.67
Now that we have the value of x, we can substitute it back into the expressions for ∠BOC and ∠AOB to find their degree measures:
∠BOC = 2x + 10 = 2(16.67) + 10 = 33.34 + 10 = 43.34 degrees
∠AOB = 4x - 15 = 4(16.67) - 15 = 66.68 - 15 = 51.68 degrees
Therefore, the degree measure of ∠BOC is approximately 43.34 degrees, and the degree measure of ∠AOB is approximately 51.68 degrees.