Sum of Angles?

Geometry Level 1

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

360 120 180 540 270

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Chew-Seong Cheong
Mar 21, 2019

The sum of the orange angles = The sum of internal angles of 4 triangles − α − β − γ − δ = 4 × 18 0 ∘ − The sum of internal angles of a quadrilateral = 4 × 18 0 ∘ − 36 0 ∘ = 360 ∘ \begin{aligned} \color{#EC7300} \text{The sum of the orange angles} & = {\color{#3D99F6} \text{The sum of internal angles of 4 triangles}} - \alpha - \beta - \gamma - \delta \\ & = {\color{#3D99F6} 4 \times 180^\circ} - \text{The sum of internal angles of a quadrilateral} \\ & = 4 \times 180^\circ - 360^\circ \\ & = \boxed{360}^\circ \end{aligned}

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