SOLUTION: In a diagram, O is the center of circle ABCD and ∠DAB=67°. Calculate the value of (i)∠DOB, (ii)∠DCB

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Question 417934: In a diagram, O is the center of circle ABCD and ∠DAB=67°. Calculate the value of (i)∠DOB, (ii)∠DCB
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!




Angle DAB is an inscribed angle subtending arc DCB.
Angle DOB is a central angle also subtending arc DCB.

An arc subtended by an inscribed angle has the measure of 
twice the measure of the inscribed angle, thus arc DCB has measure
2×67° or 134°.

A central angle has the same measure as the measure of its
subtended arc, thus angle DOB also has measure 134°.

Angle DCB is an inscribed angle subtending major arc DAB.
Since a complete circle is an arc of 360°, the measure of
arc DAB is 360°-134° or 226°.

The measure of an inscribed angle is 1/2 the measure of its
subtended arc, so angle DCB has measure 1/2 × 226° or 113°.

Edwin
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