Angle+Angle

Geometry Level 2

What is ∠ a + ∠ b \angle a+\angle b in degrees?


The answer is 45.

Fahim Muhtamim by Fahim Muhtamim , 17, Bangladesh

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1 solution

∠ a = t a n − 1 ( 1 2 ) , ∠ b = t a n − 1 ( 1 3 ) \large\angle a = tan^{-1}\Big(\frac{1}{2}\Big) , \quad\angle b = tan^{-1}\Big(\frac{1}{3}\Big)

⇒ ∠ a + ∠ b = t a n − 1 ( 1 2 ) + t a n − 1 ( 1 3 ) = t a n − 1 ( 1 2 + 1 3 1 − 1 2 ⋅ 1 3 ) = t a n − 1 ( 1 ) = 45 ° \large\Rightarrow\angle a + \angle b = tan^{-1}\Big(\frac{1}{2}\Big) + tan^{-1}\Big(\frac{1}{3}\Big) = \Large tan^{-1}\Bigg(\frac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{2}\cdot\frac{1}{3}}\Bigg) = \large tan^{-1}\Big(1\Big) = 45\degree

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