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AlgebraicAardvark

On this one, a straight line is 180º (since it's basically to 90º angles back-to-back).

Since you know the measure of angle 2 is 114º and together angle 1 and angle 2 make a straight line (or 180º), you need to know:

    114º + what = 180º

Can you take it from there?

neiby1842
The whole angle is supplementary so 180°, now just subtract 180°-114° = ?
What you get for it will be angle 1.