Question

Point B is in the interior of ∠AOC, m∠AOC = 108°, m∠AOB = 3m∠BOC. Find m∠AOB.

Answer 1

m∠AOB=81°

Explanation:

we know that

Point B is in the interior of ∠AOC

so

m∠AOC=m∠AOB+m∠BOC -----> equation A (by addition angle postulate)

we have

m∠AOC=108°

m∠AOB=3(m∠BOC)

substitute the given values in equation A and solve for m∠BOC

108°=3(m∠BOC)+m∠BOC

108°=4(m∠BOC)

m∠BOC=27°

Find the measure of m∠AOB

m∠AOB=3(m∠BOC)

substitute the measure of m∠BOC

m∠AOB=3(27°)=81°