To find the measure of angle \( f \), we can start with the relationships you provided.
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Angle \( a \) and angle \( b \) are complementary angles, which gives us the equation: \[ a + b = 90^\circ \]
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Angle \( a \) and angle \( f \) are supplementary angles, leading to the equation: \[ a + f = 180^\circ \]
Steps to Find Angle \( f \):
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Start with the equation for supplementary angles: \[ f = 180^\circ - a \]
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From the first equation \( a + b = 90^\circ \), you can express \( b \) in terms of \( a \): \[ b = 90^\circ - a \]
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Substitute this expression for \( a \) into the supplementary angle equation: \[ f = 180^\circ - a \]
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Notice that we need further information about angle \( a \) or \( b \) to isolate the value of \( f \). However, we can express all angles in terms of one of them.
You can use either \( a \) or \( b \) to find \( f \). For example, if you have a specific value for \( a \) or \( b \), substitute it back into the equations to find \( f \).
Example:
If you know \( a = 30^\circ \):
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Substitute into \( a + b = 90^\circ \): \[ 30^\circ + b = 90^\circ \rightarrow b = 60^\circ \]
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Now substitute \( a \) into \( f = 180^\circ - a \): \[ f = 180^\circ - 30^\circ = 150^\circ \]
Thus, if \( a = 30^\circ \), then \( f = 150^\circ \). You would need a similar approach if you have another known angle.