Complementary acute angles satisfy \(α=x°\) and \(β=2x°\). Solve \(x+2x=90°\), report \(\text{both}~\angle~\text{measures}\), and state the resulting sine-cosine cofunction identity.

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x = 60°, so α = 60° and β = 120°.

x = 30°, α = 30°, and β = 60°, with no cofunction identity.

x = 30°, so α = 30°, β = 60°, and sin(30°) = cos(60°).

α = 45° and β = 45°.

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Curriculum context

Course: Math II
Standard: G-SRT.7
Category: Geometry
Domain: Similarity, Right Triangles, and Trigonometry
Objective: Explain and use the complementary-angle relationship between sine and cosine.
Problem type: Find a complement and one matching cofunction identity