Maths Olympiad Prep

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Geometry Difficulty 3.6 AMC 10/12 Find the answer North Macedonia

The difference of two complementary angles α\alpha and β\beta is 20∘52′20^\circ 52'. Determine α\alpha and β\beta.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

For the angles α\alpha and β\beta we have α+β=90∘\alpha + \beta = 90^\circ and α−β=20∘52′\alpha - \beta = 20^\circ 52'. Hence β=(90∘−20∘52′):2=34∘34′\beta = (90^\circ - 20^\circ 52') : 2 = 34^\circ 34' and α=90∘−34∘34′=55∘26′.\alpha = 90^\circ - 34^\circ 34' = 55^\circ 26'.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.