Question

For #3 and #4, use the figure on the right. CB and CD are tangent to the circle. Both BA and DA connect to the center of the circle at point A.

3. What is the measurement of angle BCD

4. What is the measurement of angle ADC LABC?



​

Answer 1

3. The measurement of angle BCD is 90 degrees.

4.The measurement of angles ADC and ABC is 26.5 degrees.

For question 3:

The angle BCD can be calculated using the fact that tangents to a circle from the same point are perpendicular to each other. In this case, tangents CB and CD are perpendicular to each other, so angle BCD is a right angle. This means that angle BCD is equal to 90 degrees.

For question 4:

The angles ADC and ABC can be calculated using the interior angle sum of a triangle. We know that the sum of the interior angles of a triangle is 180 degrees, and we also know that angle A is 127 degrees. Therefore, the sum of angles ADC and ABC is:

180 degrees - 127 degrees = 53 degrees

Since angles ADC and ABC are opposite each other on the same base, they are equal. Therefore, each angle measures:

53 degrees / 2 = 26.5 degrees

Therefore, the measurement of angles ADC and ABC is 26.5 degrees.