Question

Circle theorems: Please solve for arc JK and angle 1. (Ignore the entered answers. This is a homework assignment.)

Answer 1

Answer:

$\text{Arc JK = 124}\degree$

Explanation:

Here, we want to get the value of the arc JK

To get this, we need the angle measure of the bigger arc JK that does not pass through Q

To get that, we can use the angle theorem since we have the measure of the angle that faces the arc

Mathematically, we have this as:

$2\text{ }\times\text{ m}\angle JQK\text{ = 2}\times118\degree\text{ = 236}\degree$

Now, the measure of the arc will be the difference between the larger arc and 360

This is because the larger and the smaller arc adds up to 360°

Thus, we have the measure of the arc as:

$360\degree-236\degree\text{ = 124}\degree$