Question

ab is tangent to ⊙c at point b and ad is tangent to ⊙c at point d. what is m∠a? 34° 62° 56° 124°

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, \(\angle ABC = 90^{\circ}\) and \(\angle ADC=90^{\circ}\).

Step2: Use the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \(360^{\circ}\). In quadrilateral \(ABCD\) (where \(C\) is the center of the circle), we know \(\angle ABC = 90^{\circ}\), \(\angle ADC = 90^{\circ}\), and \(\angle BCD=124^{\circ}\). Let \(\angle A=x\). Then, \(x + 90^{\circ}+124^{\circ}+90^{\circ}=360^{\circ}\).

Step3: Solve for \(x\)

First, simplify the left - hand side of the equation: \(x+90 + 124+90=x + 304\). Then, set up the equation \(x + 304=360\). Subtract \(304\) from both sides: \(x=360 - 304 = 56^{\circ}\).

Answer:

\(56^{\circ}\)