Question

What is the value of q?
A: 58
B: 122
C: 180
D: 116

Answer 1

Probably one of those, hard to choose without more details :-)

Answer 2

Okay, how much will the four angles sum to?

Answer 3

360

Answer 4

do we know anything else about the angles of a quadrilateral inscribed in a circle?

Answer 5

No

Answer 6

well, it turns out that not only do they sum to 360 degrees, but opposite angles are supplementary, so they sum to 180 degrees.

Answer 7

From that, can you figure out the values of p and q?

Answer 8

i think so

Answer 9

operators are standing by to check your answer :-)

Answer 10

is it d?

Answer 11

p is complementary with a 90 degree angle, so p + 90 = 180, so p = 180-90 = 90

we know that q and 58 degrees are complementary, so q + 58 = 180 or 180 -58 = q which means q =

Answer 12

122

Answer 13

thank you

Answer 14

take a look at this web page: http://www.mathopenref.com/quadrilateralinscribedangles.html

it has a cool gadget for demonstrating this property

Answer 15

you can even drag it into position to check your answer :-)