Question

FG Is a tangent to the circle with center A if angle DCB =15 degree and CE =DE then find angle GCE and angle BCE. CD is the diameter of the circle and B,E are on the perimeter circle joining to C

Answer 1

The first step is to draw a diagram.

Once you do that you can see that because FG is tangent to the circle, DCG and DCF form right angles.

Since DCG is a right angle and DCB is 15 degree, that means that BCG is 75 degree.

 Because vertical angles are always congruent it can be found that DCE is also 75 degree.

Therefore, BCE is 15 + 75 which is 90 degree.

Using the same logic, GCE is 75+75+15 which is 165 degree.

Answer 2

Answer:

The first step is to draw a diagram.

Once you do that you can see that because FG is tangent to the circle, DCG and DCF form right angles.

Since DCG is a right angle and DCB is 15 degree, that means that BCG is 75 degree.

 Because vertical angles are always congruent it can be found that DCE is also 75 degree.

Therefore, BCE is 15 + 75 which is 90 degree.

Using the same logic, GCE is 75+75+15 which is 165 degree.