In circle C shown below, a tangent has been drawn at point A. If m CBA   28 then explain why the measure of DAB must equal 62.

The solution is shown below

Explanation:

From the image attached:

Line BC and line AC are the radii of the circle, therefore BC = AC.

Since BC = AC, the triangle ABC is an isosceles triangle with m∠CBA = m∠CAB = 28°

Also line ED is a tangent to circle C. From the circle theorems, a tangent to a circle is at right angle to the circle radius at point of contact. Since AC is a radii, ∠EAC = 90°

Therefore:

∠DAB + ∠EAC + m∠CAB = 180° (sum of angles on a straight line)

∠DAB = 180° - ∠EAC - m∠CAB

∠DAB = 180 - 90 - 28 = 62

∠DAB = 62°

associative property of addition