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jarptica [38.1K]
3 years ago
8

What is the value of c, d, a, and b?

Mathematics
2 answers:
kaheart [24]3 years ago
6 0

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 (a+99)^{o} so:

100=1/2(a+99)

200=a+99

Subtract 99 from both sides

a=101

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

c+96=180

Subtract 96 from both sides

c=84

and,  d+100=180

d=80

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

c=1/2(a+b)

84=1/2(101+6)

168=101+b

b=67

<u>OAmalOHopeO</u>

amid [387]3 years ago
4 0

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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