Why is $\sin(155^\circ)$ same as $\sin(25^\circ)$?

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I am practicing for a test and i've come across this question which asks "What is the value of $\sin(25^\circ)$ if $\sin(155^\circ) = 0.423$?"

and I've checked on the calculator, both give same result; $0.423.$ why do they have the same value? how would you know this without using a calculator?

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2 Answers

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try drawing a circle sin is the height. You will see that at the angle 155 degrees it is the same height as 25 degrees.

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$$ \sin ( \pi - \alpha ) = \sin \pi \cos \alpha -\cos \pi \sin \alpha = \sin \alpha $$

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