Question

in circle c shown below a tangent has been drawn at point A. if measure angle CBA = 28, then explain why the measure of angle DAB must equal 62 degrees.

Answer 1

it is the complement of 28°

Explanation:

Angle DAB made by a tangent and a chord to the point of tangency is equivalent to every other inscribed angle that intercepts the same arc. Those angles have half the measure of the central angle ACB intercepting the same arc.

In isosceles triangle ABC the base angles (shown as 28°) are the complement of half the measure of the central angle. Hence angle DAB will be the complement of the angle marked 28°.

angle DAB = 90° -28° = 62°