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

Step-by-step explanation:

Lines AC and BC are radii of the circle, which means that triangle ABC is an isosceles triangle.

Since triangle ABC is an isosceles triangle, the measures of the base angles CBA and CAB are equal.

We know that the measure of angle CBA = 28º so the measure angle CAB must also equal 28º because the base angles of an isosceles triangle are equal.

Line ED is perpendicular to the radius AC and tangent to circle C at point A.

Therfore, angle EAC is equal to 90º and angle DAC is equal to 90º.

Angle DAC is made up of angle CAB and angle DAB.

So the measure of angle DAC (90º) minus the measure of angle CAB (28º) equals the measure of angle DAB.

90º - 28º = 62º

The measure of angle DAB is 62º