Question

quadrilateral OPQR is inscribed in circle N, as shown below, what is the measure of angle ROP. O(x+17),Q(6x-5),R(2x+19)

Answer 1

opposite angles in a quadrilateral inscribed in a circle are supplementary (they add up to 180 degrees)

In this quadrilateral, point O and point Q are opposite to each other, meaning they add up to 180 degrees

So,

O+Q=180

x+17 + 6x-5 =180

7x+12=180

7x=168

x=24

you are trying to find the measure of angle ROP and this is the same as angle O which was given to be x+17

But now you know x is 24 degrees so x+17 = 24+17 = 41 degrees