Sum The Green Angles

Geometry Level 1

One example of calculating the sum of a set of angles, even without knowing their individual measures, is that the three internal angles of a triangle always add to 18 0 ∘ 180^\circ . But what about other polygons or more complex figures?

What is the sum of the green angles in the image below?

18 0 ∘ 180^\circ 27 0 ∘ 270^\circ 36 0 ∘ 360^\circ 54 0 ∘ 540^\circ

Queenbe Monyei by Queenbe Monyei , 36, USA

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1 solution

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Eli Ross Staff
Dec 21, 2016

There are three triangles in this diagram, so the sum of all their interior angles is 18 0 ∘ + 18 0 ∘ + 18 0 ∘ = 54 0 ∘ . 180^\circ + 180^\circ + 180^\circ = 540^\circ. The three unshaded angles at the bottom form a straight angle with a measure of 18 0 ∘ . 180^\circ. The total measure of the green angles is the measure of all interior angles minus the measure of the straight angle: 54 0 ∘ − 18 0 ∘ = 36 0 ∘ . 540^\circ - 180^\circ = 360^\circ.

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