Beam OC is bisector of swept angle AOB. Angle EOF is straight, angle EOC = 25 degrees. Find the degree measure of the angles AOE, COF and FOB. Write down equal angles.
Beam OC is the bisector of the swept angle AOB, which means that the angle AOB is 180 degrees. The EOF is straight, which means it is 90 degrees, the EOC is 25 degrees.
The angle EOF is straight, which means it is 90 degrees and consists of the sum of the angles EOC and COF, we find the angle COF:
COF = EOF – EOC;
COF = 90 – 25 = 65 (degrees).
The AOC angle is equal to the COB angle and is equal to 90 degrees. Find the AOE angle:
AOE = AOC – EOC;
AOE = 90 – 25 = 65 (degrees).
Let’s find the angle FOB, for this it is necessary to subtract the angle COF from the COB angle.
FOB = COB – COF;
FOB = 90 – 65 = 25 (degrees).
Answer: AOE = COF = 65 degrees, EOC = FOB = 25 degrees.
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