What is the value of c, d, a, and b?
2 answers:
Answer:
By the inscribed angle theorem, the measure of inscribed angles is half the measure of its intercepted arc, the inscribed angle measuring 100°.
Intercepts the arc measuring
so:


Subtract 99 from both sides

By the corollary 3 of the inscribed angle theorem, the opposite angle of a quadrilateral inscribed in a circle are supplementary so:

Subtract 96 from both sides

and, 

The inscribed angle measuring c° intercepts the arc measuring (a+b)° so:




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Answer:
a=101
b=67
c=84
d=80
Step-by-step explanation:
The measure of an intercepted arc will always be twice the measure of the inscribed angle
to find A:
2(100)=a+99
200=a+99
a=101 degrees
d=80 degrees because 100*2=200, 360-200=160, and 160/2=80
You can find c by subtracting 100, 96, and 80 from 360 and you get c=84 degrees
Find the measure of b by using what you found as measure of c and a
2(84)=101+b
168=101+b
b=67
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