Question

I need help with this I also need to show my work in order to get credit

Answer 1

We want to find the measure of arc AD. We would need to find x first as this would guide us toward finding AD.

We know from a circle geometry theorem that;

I. Angles in the same segment are equal. In this case,

`\angle ABD\approx\angle ACD`

Therefore, we can equate them, equating them we obtain;

`\begin{gathered} 11x-3=8x+15 \\ 11x-8x=15+3 \\ 3x=18 \\ x=6 \end{gathered}`

We could use this to obtain the measures of angle ABD or ACD, obtaining one is enough as they are congruent, let us use
`\begin{gathered} \angle ABD=11x-3 \\ =11(6)-3_{} \\ =66-3 \\ =63^o \end{gathered}`We can therefore find the measure of angle AD, by using the circle geometry theorem;

ii. Angles subtended at the centre of a circle is twice that subtended at the circumference;

Thus;

`\begin{gathered} \angle AED=2\angle ACD \\ \angle AED=2(63) \\ \angle AED=126^o \end{gathered}`

Therefore, the measure of arc AD is 126 degrees.