Question

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

Answer 1

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

Step-by-step 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{ }*\text{ m}\angle JQK\text{ = 2}*118\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`