To find the value of \( c \) given the angles \( 144° \) and \( (6c)° \), we need to understand the relationship between these angles.
Since \( 144° \) and \( 6c° \) are likely part of a supplementary relationship (summing to \( 180° \)) or complementary (summing to \( 90° \)), we can set them equal to:
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If they are supplementary: \[ 144° + 6c° = 180° \]
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If they are complementary: \[ 144° + 6c° = 90° \]
Let's start with the supplementary case: \[ 144 + 6c = 180 \] Subtract \( 144 \) from both sides: \[ 6c = 180 - 144 \] \[ 6c = 36 \] Now, divide by \( 6 \): \[ c = \frac{36}{6} = 6° \]
Now, let's check the complementary case for completeness: \[ 144 + 6c = 90 \] Subtract \( 144 \) from both sides: \[ 6c = 90 - 144 \] \[ 6c = -54 \] Dividing by \( 6 \) gives: \[ c = -9° \]
Since negative angles generally do not fit within the standard context of geometry relating to angle measures, we can conclude that the most appropriate solution is from the supplementary angles scenario.
Thus, the value of \( c \) is: \[ \boxed{6°} \]