Question

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

Answer 1

thats not it

Answer 2

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.

Answer 3

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.