Question

A quadrilateral (Not Regular) is inscribed in a circle. One of the angles is 82°, find the angle that is opposite the given angle. Show all calculations.

Answer 1

the sum of opposite angles of a quadrilateral inscribed in a circle is 180 deg

Answer 2

Thanks:)

Answer 3

do you want to see a proof ?

Answer 4

sure :) that would also help me.

Answer 5

so first we need to use the relation between arc length and angle
I hope you know it :
arclength = angle * radius
?

Answer 6

Yes I get that part

Answer 7

good
now :

Answer 8

since we measure the angles from the sides of the circle and not from its center
the are lengths are multiplied by 2 for each of those angles!

so as you can see
the angle C can give us arc XYZ length :
arclength(XYZ) = 2* C * r

and the angle A can give us arc ZWX lenght:
arclength(ZWX) = 2* A * r

now we can use the fact that the arcs together completes the circle

arclength(XYZ) + arclength(ZWX) = 360 * r ( in fact we usually write 2*pi*r)

so we have
2*C*r + 2*A*r = 360*r
A+C = 180

Answer 9

Wow thanks I get It You explained it really good. Your amazing :)

Answer 10

the multiplication by 2 is a bit tricky
almost missed it myself lol

Answer 11

lol :)