Given the quadrilateral RSTO inscribed in the circle with O as centre. Find the size angle x and given RST = 60o

Given the quadrilateral RSTO inscribed in the circle with O as centre. Find the size angle x and given RST = 60o

Answer Details

To find the size of angle x, we can start by using the fact that the sum of the opposite angles in an inscribed quadrilateral is 180 degrees. In this case, angle RST is opposite to angle O, and angle OST is opposite to angle x. We are given that angle RST is 60 degrees, so we can use this to find angle O: angle RST + angle RTO + angle STO + angle OST = 360 degrees 60 + angle RTO + angle STO + angle OST = 360 angle RTO + angle STO + angle OST = 300 Since angle RTO and angle STO are both equal to angle O (because they are both subtended by the same arc), we can write: 3 x angle O = 300 angle O = 100 degrees Now that we know angle O, we can find angle x: angle OST = 180 - angle RST - angle O angle OST = 180 - 60 - 100 angle OST = 20 degrees Therefore, the size of angle x is 20 degrees, which corresponds to option D.