Sum of Angles!

Geometry Level 1

What is the sum of the orange angles (in degrees)?

120 450 180 360 720

Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

Chew-Seong Cheong
Sep 26, 2018

The sum of the eight orange angles S = sum of angles of 4 triangles − ( α + β + γ + δ ) S = \text{sum of angles of 4 triangles} - (\alpha + \beta + \gamma + \delta) . And we note that α + β + γ + δ = sum of angles of a quadrilateral \alpha + \beta + \gamma + \delta = \text{sum of angles of a quadrilateral} . Therefore, S = 4 × 18 0 ∘ − 36 0 ∘ = 360 ∘ S = 4\times 180^\circ - 360^\circ = \boxed{360}^\circ .

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Thank you for sharing your solution.

Hana Wehbi - 2 years, 8 months ago

Chew, nice solution. I did the same. Ed Gray

Edwin Gray - 2 years, 8 months ago
Krishna Karthik
Oct 18, 2018

We know that the sum of all angles in a quadrilateral is 360 degrees, therefore the sum of all the orange angles are

180 ( 4 − 2 ) 180(4-2) = 360 degrees

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