Question

In circle K, what is the value of x? 75° x = 30° O x = 25° O X = 20° O x = 15° 1

Answer 1

`x\text{ = 15}`

Here, we want to get the value of the angle marked x

As we can see, the side marked k represent the center of the circle. Hence it is the midpoint of the diameter of the circle

This means the angle at k is 180 degrees since the sum of angles on a straight line is 180

The value of the angle that faces k in the triangle is 90 degrees. This is because angle at the center is twice that of that at the circumference

So, we have the two angles of the triangle and we need the last

Mathematically, the sum of angles in a triangle is 180

Thus;

`\begin{gathered} 75+\text{ x + 90 = 180} \\ x\text{ = 180-90-75} \\ x\text{ = 15} \end{gathered}`