Question

0-19 B The points A, B, and C on the circle with center O in the figure are such that ZBOC = 30° and ZAOB = 60°. If D is a point on the circle other than the arc ABC, find ZADC. ​

Answer 1

Answer:

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refer the reference diagram uploaded above

Step-by-step explanation:

so here for an adjoining circle with centre O

Angle AOB and Angle BOC are the central angles

so we know that

Measure of central angle is same as that of the arc intercepted by it on the circumference of circle

thus then

Angle AOB=m(arc AB)=60°

Angle BOC=m(arc BC)=30°

so now then

By using arc addition property

we get

m(arc AC)=m(arc AB)+m(arc BC)

=60+30

=90 degrees

so here angle ADC intercepts arc AC on circumference of circle

so by inscribed angle theorem

we get

Angle ADC=1/2×m(arc AC)

=1/2×90

=45 degrees

hence Angle ADC=45 degrees