Angle AOB and BOC are adjacent, OM is the bisector of angle AOB. Find MOB Angle if Angle AOB: BOC = 5: 4.


1) We know that two adjacent angles relate to each other as 5: 4, and the sum of adjacent angles is 180 °. If we introduce the proportionality coefficient – x into the ratio, then the equation can be drawn up 5x + 4x = 180 °. Using it, we find the angle AOB = 100 °.

2) Since the ray MO is the bisector of the angle AOB (it divides the angle in half), then we only need to divide the found angle AOB = 100 ° in half and get the desired angle of the MB.

Answer: 50 °.

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