The measure of m<JMO is 20 degrees
The triangle JOK is a 60 degrees equilateral triangle. Hence the measure of m<O at the center is 60 degrees.
Angle at a point
- The sum of the angle at a point is 360 degrees.
Since the base angles of triangle KOL and OLM are equal hence;
- m<KOL + m<MOL + m<JOM + m<JOK = 360 (angle at a point)
Substitute the base angles and the equilateral angles to get angle JOM
80 + 80 + m<JOM + 60 = 360
m<JOM = 360 - 360 - 220
m<JOM = 140 degrees
Sum of angles in a triangle
Since the sum of angle in the triangle JOM is 180 degrees, hence;
2m<JMO + m<JOM = 180
2m<JMO = 180 - 140
2m<JMO = 40
m<JMO = 20 degrees
Hence the measure of m<JMO is 20 degrees
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