Question

Find the measure of an angle indicated?

Answer 1

The measure of the angle indicated by the question mark is 68 degrees. This is determined by the property of inscribed angles, where the measure is half of the intercepted central angle.

In the given scenario, the inscribed angle, denoted by the question mark, intercepts the same arc as the central angle
`$\angle{FLG}$` within the circle. According to the properties of inscribed angles, the measure of an inscribed angle is half the measure of the central angle it intercepts.

Given that
`$\angle{FLG}$` has a measure of
`$136^\circ$`, we can apply the rule to find the measure of the inscribed angle:

`\[\text{Measure of inscribed angle} = (1)/(2) \cdot \text{Measure of central angle} = (1)/(2) \cdot 136^\circ = 68^\circ\]`

Therefore, the angle indicated by the question mark is
`$68^\circ$`. This is because an inscribed angle in a circle provides a unique and consistent relationship with its intercepted central angle, making it a valuable property in circle geometry. The inscribed angle theorem simplifies angle calculations in circular contexts, contributing to a deeper understanding of geometric principles.
The probable question may be:

Find the measure of the angle indicated with a question mark.