Question

Given that O is the centre of the circle, find the values of x and y

Answer 1

We know that the angle at the top of the triangle is 90 degrees by definition
(Angle in the Semicircle Theorem). That makes angle y 45 degrees (as is the angle opposite y). The angle next to 82 degrees is supplementary and therefore is 98 degrees. Since we know we have 98, and 45 degree angles in the triangle already, x must be 37. Since the triangle must have 180 degrees.

Y = 45
X = 37

Answer 2

Let AB be the diameter trough O the center & C the vertex of the triangle.

1)Since this triangle is inscribed in half a circle, means that it is a right triangle

2)Triangle AOC is isosceles (AO=OC=Radius)  ==> angle y = OCA

Since the sum of angles in any triangle is 180 & angle O =

82 then y =(180-82)/2 =49 (y=49).

The angle ACB =90 & x=90-49 =51, then x= 51