Question

Find the measure of m

Answer 1

The measure of angle EOF is;

`m\angle EOF=74^(\circ)`

Step-by-step explanation:

Given the circle in the attached image.

We can see the line EH and FJ Intersect each other at the center.

So, Angle EOF and Angle HOJ form vertically opposite angles.

Recall that vertically opposite angles are congruent;

`\begin{gathered} \angle EOF\cong\angle HOJ \\ m\angle EOF=m\angle HOJ \end{gathered}`

From the figure, the measure of angle HOJ is given;

`m\angle HOJ=74^(\circ)`

Therefore;

`\begin{gathered} \text{ Since,} \\ m\angle EOF=m\angle HOJ \\ \text{and } \\ m\angle HOJ=74^(\circ) \\ \text{then;} \\ m\angle EOF=74^(\circ) \end{gathered}`

The measure of angle EOF is;

`m\angle EOF=74^(\circ)`