Question

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

Answer 1

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

Answer 2

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:

$c=1/2(a+b)$

$84=1/2(101+6)$

$168=101+b$

$b=67$

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