ABCD Is quadrilateral inscribed in a circle such that BC =9cm ,BA=7.2cm,CBA=51 and ACD=29 calculate angle AC

Answer 1

To find angle AC, we need to use the property of an inscribed angle.

An inscribed angle is half the measure of the arc it intercepts.

Since ABCD is inscribed in a circle, we can see that angle ADC is the intercepted arc for angle AC.

Thus, angle AC = 2 * angle ADC.

Now, let's find angle ADC.

We know that angle DCA = angle DCB = 180 - angle CBA = 180 - 51 = 129 degrees.

Since ABCD is a quadrilateral, the sum of all interior angles is 360 degrees.

Thus, angle ADC + angle DCA = 360 degrees.

Substituting the values we know, we have:

angle ADC + 129 = 360

Subtracting 129 from both sides, we get:

angle ADC = 231 degrees.

Finally, substituting this value into our initial equation, we have:

angle AC = 2 * 231 = 462 degrees.

Therefore, angle AC is equal to 462 degrees.