Question

GEOMETRY 100POINTS!!!!​

Answer 1

C) 318°

Explanation:

Answer 2

C) 318°

Explanation:

Line segment LM appears to be a diameter of the circle.

As angles on a straight line sum to 180°, and an arc measure is equal to its corresponding central angle measure, then the value of x can be calculated as follows:

`\begin{aligned}\overline{LM}&=180^(\circ)\\\overset{\frown}{JK}+\overset{\frown}{KL}+\overset{\frown}{LM}&=180^(\circ)\\(x+96)^(\circ)+47^(\circ)+(x+47)^(\circ)&=180^(\circ)\\x+96+47+x+47&=180\\2x+190&=180\\2x&=-10\\x&=-5\end{aligned}`

Therefore, the measure of minor arc JK is:

`\begin{aligned}\overline{JK}&=x+96\\&=-5+96\\&=91^(\circ)\end{aligned}`

The name of an arc is derived from the points used to define it.

Major arcs (greater than 180°) are always named with three letters: the starting point of the arc, a point on the arc, and the endpoint of the arc.

Therefore, arc JLI is the sum of the minor arcs JK, KL, LM and MI:

`\overset{\frown}{JLI}=\overset{\frown}{JK}+\overset{\frown}{KL}+\overset{\frown}{LM}+\overset{\frown}{MI}`

We know that JK = 91° and KL = 47°.

As line segment LI appears to be the diameter, the sum of minor arcs LM and MI is 180°. Therefore:

`\begin{aligned}\overset{\frown}{JLI}&=\overset{\frown}{JK}+\overset{\frown}{KL}+\overset{\frown}{LM}+\overset{\frown}{MI}\\&=91^(\circ)+47^(\circ)+180^(\circ)\\&= 318^(\circ)\end{aligned}`

Therefore, the measure of the major arc JLI is 318°.