Question

the graph on the right shows two angles that share the same terminal side: ( 45^{circ} ) and ( -315^{circ} ). together, the angles form a circle. what if you subtract the angle measures? ( 45^{circ}-(-315^{circ})=square^{circ} ) ( -315^{circ}-45^{circ}=square^{circ} )

Explanation:

Step1: Simplify the first subtraction

To subtract a negative angle, we use the rule \( a - (-b)=a + b \). So for \( 45^\circ-(-315^\circ) \), we have \( 45^\circ + 315^\circ \).
\( 45^\circ+315^\circ = 360^\circ \)

Step2: Simplify the second subtraction

For \( -315^\circ - 45^\circ \), we just add the magnitudes with the negative sign.
\( -315^\circ-45^\circ=- (315^\circ + 45^\circ)=-360^\circ \)

Answer:

First blank: \( 360^\circ \)
Second blank: \( -360^\circ \)