Question

in each of the following figures O is the center of the circle find the size of the each lettered angle​

Answer 1

In the figure,

AC is the diameter of circle with centre O

∠DAC=37°

AD || BC

∠ACB=∠DAC (Alternate angles)

Hence,

x=37°

In Δ ABC,

∠B=90° (angle in semicircle)

By angle sum property of triangle, we get,

∠x+∠y+∠B=180°

37°+∠y+90°=180°

∠y=180°−127°

We get,

∠y=53°