Question

In exercises $8-13$ find the angle or the arc named.

$\angle GQE$

Short answer

The measure of angle $\angle GQE$ is $110°.$

Step-by-step solution

Step 1. Given information:

The given figure is,

Step 2. Concept used:

In the circle the arc of the given circle is equals to the angle that is asked.

In the circle the arc of the circle can be calculated by adding the arcs of the circle related to it.

Step 3. Applying the concept:

Here, we can see in the figure

$\begin{array}{l}m\stackrel{⏜}{GE}=m\stackrel{⏜}{GF}+m\stackrel{⏜}{FE}\\ \text{=}{60}^{\circ }+{50}^{\circ }\\ \text{=}{110}^{\circ }\end{array}$

As we know,

$\begin{array}{l}m\angle GQE=m\stackrel{⏜}{GE}\\ {\text{=110}}^{\circ }\end{array}$

Therefore, the measure of the angle $\angle GQE$ is $50°.$