Question

Quadrilateral OPQR is inscribed inside a circle as shown below. Write a proof showing that angles O and Q are supplementary

Answer 1

As anoutline, angles O and Q are inscribed angles which are measured by one-half of its intercepted arc.

angle O = 1/2 arc RQP
angle Q = 1/2 arc ROP

so arcs RQP and ROP together make up the entire circle which has 360 degrees.

so angles O and Q is 1/2 (360) = 180 degrees (supplementary angles).

Answer 2

thank you

Answer 3

welcome.

Answer 4

@jim_thompson5910 Hey jim, can you help me understand this a little better? I don't understand what he is saying

Answer 5

you'll have to be more specific

Answer 6

I don't see how "so angles O and Q is 1/2 (360) = 180 degrees (supplementary angles)."

Answer 7

that's basically saying that angles O and Q add up to 180 degrees

ie O + Q = 180

Answer 8

the arcs form a complete 360 degree circle and there is no overlap or gaps

so the inscribed angles will add up to half of this (because you take half of the arcs to get the inscribed angle)