angle abd measures (4x + 10)°. angle acd measures (5x - 2)°. what is the measure of arc ad? 12° 58° 96° 116°

Answer:

D. $116^{\circ}$

Explanation:

Step1: Use inscribed - angle theorem

Inscribed angles subtended by the same arc are equal. So, $\angle ABD=\angle ACD$. $4x + 10=5x - 2$

Step2: Solve for $x$

Subtract $4x$ from both sides: $10=x - 2$. Add 2 to both sides: $x = 12$.

Step3: Find the measure of an inscribed angle

Substitute $x = 12$ into the measure of $\angle ABD$: $\angle ABD=4x + 10=4\times12+10=48 + 10=58^{\circ}$.

Step4: Find the measure of the arc

The measure of an arc is twice the measure of the inscribed - angle subtended by it. So, the measure of arc $AD = 2\angle ABD=2\times58^{\circ}=116^{\circ}$.