as the baseline of the abd triangle is a diameter of the circle (it goes through the center of the circle), c is the supplementary angle to 76° (it adds up to 180°), as c + 76 represents a half-circle.

c = 180 - 76 = 104°

the circle theorem says : the angle at the center is twice the angle at the circumference.

therefore a = 76/2 = 38°

similarly,

b = 104/2 = 52°

and remembering that the sum of all angles in a triangle is always 180°

d = 180 - 38 - 52 = 90°

which is true also, because all inscribed triangles in a half- circle with the baseline being the diameter, must be right-angled.

Step-by-step explanation:as the baseline of the abd triangle is a diameter of the circle (it goes through the center of the circle), c is the supplementary angle to 76° (it adds up to 180°), as c + 76 represents a half-circle.

c = 180 - 76 = 104°

the circle theorem says : the angle at the center is twice the angle at the circumference.

therefore a = 76/2 = 38°

similarly,

b = 104/2 = 52°

and remembering that the sum of all angles in a triangle is always 180°

d = 180 - 38 - 52 = 90°

which is true also, because all inscribed triangles in a half- circle with the baseline being the diameter, must be right-angled.