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Question Number 189557 by normans last updated on 18/Mar/23

Answered by mr W last updated on 18/Mar/23

Commented by mr W last updated on 18/Mar/23

θ=180°−2α−2β    =180°−2(α+β)    =180°−2×45°    =90°

$$\theta=\mathrm{180}°−\mathrm{2}\alpha−\mathrm{2}\beta \\ $$$$\:\:=\mathrm{180}°−\mathrm{2}\left(\alpha+\beta\right) \\ $$$$\:\:=\mathrm{180}°−\mathrm{2}×\mathrm{45}° \\ $$$$\:\:=\mathrm{90}° \\ $$

Answered by HeferH last updated on 18/Mar/23

 α+β = 135°   180°−α + 180°−β + 45° + x = 360°   x = (α +β)− 45° = 135° − 45° = 90°   x = 90°

$$\:\alpha+\beta\:=\:\mathrm{135}° \\ $$$$\:\mathrm{180}°−\alpha\:+\:\mathrm{180}°−\beta\:+\:\mathrm{45}°\:+\:\mathrm{x}\:=\:\mathrm{360}° \\ $$$$\:\mathrm{x}\:=\:\left(\alpha\:+\beta\right)−\:\mathrm{45}°\:=\:\mathrm{135}°\:−\:\mathrm{45}°\:=\:\mathrm{90}° \\ $$$$\:\mathrm{x}\:=\:\mathrm{90}° \\ $$

Commented by HeferH last updated on 18/Mar/23

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