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

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## Answers

Image of the circle is attached. Answer:Measure of angle G = 36°Step-by-step explanation:From the question, we are told the arc GF has a measure of 108°, i.em∠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 ΘWhere, A = length of arcr = radiusΘ = 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 = [tex] \frac{72}{2} = 36 [/tex] m∠G = 36°Measure of angle G = 36°