Question

Here's another geometry thing I suck at...

Find the value of each variable. For the circle, the dot represents the center.

Answer 1

a = 133; b = 31; c = 82; d = 64.
Opposite angles in an inscribed quadrilateral are supplementary; this means that d + 116 = 180. Subtracting 116 from both sides, we have d = 64.

By the same theorem, c + 98 = 180; subtracting 98 from both sides, we have c = 82.

Inscribed angles are equal to 1/2 the measure of the intercepted arc. Using this, we have

116 = 1/2(a+99)

Multiplying both sides by 2, we have
232 = a+99

Subtract 99 from both sides:
232 - 99 = a + 99 - 99
133 = a

We also have that
82 = 1/2(133+b)

Multiplying both sides by 2, we have:
164 = 133 + b

Subtract 133 from both sides:
164 - 133 = 133 + b - 133
31 = b