Question

The circle below has a center H. Suppose measurement IJ=68°. What is measurement IGJ?

Answer 1

Step-by-step explanation:

Given;

We are given a circle with center H. Also we are given the angle measure of arc IJ.

Required;

We are required to calculate the angle measure of IGJ from the information given.

Step-by-step solution;

First of all, take note that the angle at the center of a circle is twice the angle at the circumference.

Also, we should take note that the measure of the central angle is the same as the angle measure of the arc subtended by the radii of the central angle. This means

`m(arcIJ)=\angle IHJ`

Therefore if the arc measure IJ is 68 degrees, then

`\angle IHJ=68\degree`

We now have the angle at the center as 68 degrees. The angle at the circumference, which is angle IGJ will now be;

`\angle IHJ=2*\angle IGJ`

We now divide both sides by 2;

`\begin{gathered} (\angle IHJ)/(2)=\angle IGJ \\ \\ (68)/(2)=\angle IGJ \\ \\ 34=\angle IGJ \end{gathered}`

ANSWER:

`m\angle IGJ=34\degree`