Many angles to add

Geometry Level pending

Shown above is a circle with center at O O . If ∠ A O J = 4 0 ∘ \angle AOJ=40^\circ , find the sum of the missing angles (in degrees).

More problems

21 0 ∘ 210^\circ 36 0 ∘ 360^\circ 18 0 ∘ 180^\circ 14 0 ∘ 140^\circ

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1 solution

Relevant wiki: Circles - Area

The central angle is 4 0 ∘ 40^\circ so each inscribed angle is 2 0 ∘ 20^\circ because they intercept the same arc. Therefore, the desired answer is 7 × 20 = 14 0 ∘ 7 \times 20 = 140^\circ

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