Question

Study the diagram of circle O.

The measure of arc JK is 77º and mZHOI = 44º.
46
J
77°
H
1
449
K
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If mIJ = 46°, what is the measure of angle HOK?

Answer 1

∠ HOK = 167°

Explanation:

The central angle is equal to the measure of the arc that subtends it , so

∠ IOJ = arc IJ = 46°

∠ LOK = arc JK = 77°

Then

∠ HOK = ∠ HOI + ∠ IOJ + ∠ LOK = 44° + 46° + 77° = 167°