Question

AB and BC are tangents of the circle with the center at D. The measure of ACD = 25°. Which is the measure of ABC? (IMAGE ATTACHED)
A. 25°
B. 50°
C. 90°
D. 130°

Answer 1

Hint: Remember that the length of AC = length of CD. This is because they are both radii of the same circle. Therefore, Triangle ACD is an equilateral triangle, with angle(ACD)=angle(CAD)=25degrees.
 
From there, we can work out the angle of ADC: 180-25-25=130 degrees.

Now, expand our scope, and look at the quadrilateral ABCD. We have two right angles in this quadrilateral, because of the tangency of two of the sides with the circle. So to work out the required angle(ABC), just take subtract 2*90degrees and angle(ADC)=130deg from 360deg (which is the sum of all angles of a quadrilateral. Then we have the answer: 50degrees