Question

Line segment OC splits ∠AOB into two angles. Find ∠AOC if m∠AOB = 155°, and m∠COB is 15° less than m∠AOC.

a) 75°
b) 80°
c) 85°
d) 90°

Answer 1

To find the measure of angle AOC, subtract the measure of angle COB from angle AOB. Given that m∠AOB = 155° and m∠COB is 15° less than m∠AOC, we can set up the equation: m∠AOB - m∠COB = m∠AOC. By solving the equation, we find that m∠AOC ≈ 85°.

Step-by-step explanation:

To find the measure of angle AOC, we need to subtract the measure of angle COB from angle AOB. Given that m∠AOB = 155° and m∠COB is 15° less than m∠AOC, we can set up the equation: m∠AOB - m∠COB = m∠AOC. Substituting the given values, we have 155° - m∠COB = m∠AOC. Now we need to solve for m∠COB. We can set up another equation: m∠COB = m∠AOC - 15°. Substituting this into the first equation, we have 155° - (m∠AOC - 15°) = m∠AOC. Simplifying, we get 170° - m∠AOC = m∠AOC. Solving for m∠AOC, we find that m∠AOC ≈ 85°.