What is the size of the unknown angle?

What is the size of the unknown angle?
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[@Ramkabharosa]

Let θ= the unknow angle, the equal lengths be a & the median be b. Then by the Sine Rule,
sin(θ) /a = sin(135°-θ) /b (Eq.1) & sin(15°) /a = sin(30°) /b (Eq.2). Dividing Eq.1 by Eq.2
gives sin(θ)/sin(15°) = sin(135°-θ)/sin(30°). So sin(θ).(½) = sin{180-(135°-θ)}.sin(15°) =
sin(45+θ).sin(15°) = (1/√2).{sin(θ) + cos(θ)}.sin(15°) ∴ tan(θ).{(½) - (1/√2).(√3-1)/2√2} =
(1/√2).(√3-1)/2√2. So tan(θ).{√3.(√3-1)/4} = (√3-1)/4. Hence tan(θ) = 1/√3 & thus θ = 30°.
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