Given that arc GF has a measure of 108°, what is the measure of angle G?

Image of the circle is attached.

Measure of angle G = 36°

Step-by-step explanation:

From the question, we are told the arc GF has a measure of 108°, i.e

m∠GF = 108°

From the circle, we can see a part of the circumference of the circle is the arc length (curve from point G to point F).

The arc length can be said to be the measure of the distance between two points along the section of a curved line which makes up an arc.

The arc length is expressed as:

A = r x Θ

Where,

A = length of arc

r = radius

Θ = arc

The measure of the central angle intercepting an arc is equal to the degree measure of the arc.

Here, the degree measure of the arc is 108° since it is equal to the central angle, E, the measure of angle E is 108°. ie m∠E = 108°

We know the total sum of angles of a triangle is 180°.

Therefore,

m∠E + m∠F + m∠G = 180°

108° + m∠F + m∠G = 180°

m∠F + m∠G = 180° - 108°

m∠F + m∠G = 72°

From the diagram we could see that F and G are parallel to each other, which means they have equal angles. Therefore, m∠F = m∠G.

Since they are equal,

m∠G =

m∠G = 36°

Measure of angle G = 36°

i dont know sorry

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