Question

If the measure of arc BC is 182 degrees and the measure of arc AC is 78 degrees, what is the measure of angle 1?O 91 degrees52 degrees104 degrees78 degrees

Answer 1

It is given that the measure of arc BC is 182 degrees

that is

`b=182^0`

the measure of arc AC is 78 degrees.

That is

`a=78^0`

We know that

`\angle1=(1)/(2)(b-a)`

Hence

`\begin{gathered} \angle1=(1)/(2)(182^0-78^0) \\ \\ \angle1=(1)/(2)(104) \\ \angle1=52^0 \end{gathered}`

Hence 52 degrees is the correct answer.