Question

ab is tangent to ⊙c. find m∠a. enter deg after any value that is in degrees.

Explanation:

Step1: Recall tangent - radius property

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

Step2: Use triangle angle sum property

In triangle \( CBA \), the sum of interior angles is \( 180^{\circ} \). We know \( \angle CBA = 90^{\circ} \) and \( \angle BCA = 58^{\circ} \). Let \( \angle A=x \). Then, \( x + 90^{\circ}+ 58^{\circ}=180^{\circ} \).

Step3: Solve for \( x \)

Simplify the equation: \( x=180^{\circ}-90^{\circ}-58^{\circ} \). Calculate \( 180 - 90 - 58 = 32 \). So, \( \angle A = 32^{\circ} \).

Answer:

\( 32 \)