Question

given circle o with center d and diameter ac in the figure below, find each angle measure. m(∠1) = m(∠2) = 60° m(∠3) = m(∠4) = 60° m(∠5) = 30° (type whole numbers )

Explanation:

Step1: Recall circle - radius property

Since DA = DB (radii of the same circle), $\triangle$ DAB is isosceles. So, m($\angle$1)=m($\angle$5). Given m($\angle$5) = 30$^{\circ}$, then m($\angle$1)=30$^{\circ}$.

Step2: Use angle - sum property of a triangle in $\triangle$ ADC

In $\triangle$ ADC, DA = DC (radii of the same circle). $\angle$A = 30$^{\circ}$, and since $\triangle$ ADC is isosceles, $\angle$3 = $\angle$A = 30$^{\circ}$.

Answer:

m($\angle$1)=30$^{\circ}$
m($\angle$3)=30$^{\circ}$