Question

select the correct answer from each drop - down menu.for circle o, ( mwidehat{cd}=125^{circ}) and ( angle abc = 55^{circ}).in the figure, (angle) and (angle) have measures equal to ( 35^{circ}).

Explanation:

Step1: Find \(\angle CAD\)

Since \(CD = 125^{\circ}\), the central angle \(\angle COD=125^{\circ}\). The inscribed angle \(\angle CAD=\frac{1}{2}(180^{\circ}-\angle COD)\). Substitute \(\angle COD = 125^{\circ}\) into the formula: \(\angle CAD=\frac{1}{2}(180 - 125)=\frac{1}{2}\times55 = 35^{\circ}\)

Step2: Find \(\angle CAB\)

We know that \(\angle ABC = 55^{\circ}\). In \(\triangle ABC\), \(\angle CAB=90^{\circ}-\angle ABC\) (angle between tangent and radius is \(90^{\circ}\)). Substitute \(\angle ABC = 55^{\circ}\) into the formula: \(\angle CAB=90 - 55=35^{\circ}\)

Answer:

\(\angle CAD\) and \(\angle CAB\)