The central angle aob is 36 ° greater than the inscribed angle acb. Find the angle acb.
| March 1, 2021 | education
Since the inscribed angle ACB and the central angle AOB rest on the same arc AB, the angle AOB is twice the angle ACB.
AOB = 2 * ACB. (one)
By condition, the angle AOB is 36 more than the angle ACB.
AOB = ACB + 36. (2)
Let’s solve the system of equations 1 and 2.
ACB + 36 = 2 * ACB.
ACB = 36.
Then the angle AOB = 2 * 36 = 72.
Answer: Angle ACB is 36.
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