Question

On circle O below, the measure of FJ is 84. The measure of GH is 76º.

What is the measure of HKJ?

Answer 1

HKJ = 100°

Explanation:

In this problem we need to use the property of a inscribed angle:

The inscribed angle is a point in the circle that has endpoints also in the circle. The value of the inscribed angle is half the value of the arc formed by the endpoints.

So, If the arc FJ is 84°, we have that the angle in point G isi 84/2 = 42°

If the arc GH is 76°, we have that the angle in point F is 76/2 = 38°

Now, in the triangle GFK, we have that the sum of internal angles of triangle is 180°, so:

GKF + 42 + 38 = 180

GKF = 100°

The angle GKF is identical to the angle HKJ, because they are vertically opposite angles, so:

HKJ = 100°