line NO is tangent to the circle at N and the measure of the arc LM is 64º. What is the measure of ∠MNO?
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Answer:
31.98
Step-by-step explanation:
The circumference of the circle is 96 units.
Therefore, 2π×r=96
⇒r=
2×22
96×7
=15.27 units
Now, in the quadrilateral OLMN,∠OLM+∠LMN+∠MNO+∠NOL=360
o
Given that LM and MN are tangents to the circle, ∠OLM=∠ONM=90
o
∴∠NOL=360−90−90−60=120
o
The length of arc is given by rθ where θ is the angle made by the arc at the centre in radian.
Thus, arc length LN=15.27×
180
120π
=31.98 units.
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