Ray oc divides ∠aob into two angles. find the measurement of ∠aoc, if m∠aob = 155°, and m∠aoc is by 15° greater than m∠cob.

We are given that:

m∠AOB = m∠AOC + m∠COB

We are also given that:

m∠AOC = m∠COB + 15

m∠AOB = 155

Therefore:

155 = m∠COB + 15 + m∠COB

2 m∠COB = 140

m∠COB = 70°

and,

m∠AOC = m∠COB + 15 = 85°

 

Answers:

m∠COB = 70°

m∠AOC = 85°

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