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Two complementary angles have measures of $s$ and $t$ . If $t$ is less than twice $s$ , which system of linear equations can be used to determine the measure of each angle

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Complementary angle identities

Full solution

Q. Two complementary angles have measures of

s

and

t

. If

t

is less than twice

s

, which system of linear equations can be used to determine the measure of each angle

Equation Setup: Since the angles are complementary, their measures add up to $90$ degrees. So, we have the equation: $\newline$ $s + t = 90$
Inequality Statement: The problem states that $t$ is less than twice $s$ , which can be written as: $\newline$ $t < 2s$ $\newline$ But since we need an equation, we'll use: $\newline$ $t = 2s - k$ , where $k$ is a positive number.
System of Equations: Now we have a system of two equations: $\newline$ $1$ ) $s + t = 90$ $\newline$ $2$ ) $t = 2s - k$ $\newline$ We can't solve for $k$ since we don't have enough information, but we can use these two equations to express $t$ in terms of $s$ .
Eliminate Variable: Substitute the second equation into the first to eliminate $t$ : $s + (2s - k) = 90$
Correcting Mistake: Combine like terms: $3s - k = 90$
Correcting Mistake: Combine like terms: $3s - k = 90$ We realize we made a mistake because we can't solve for two variables with just one equation. We need to correct the second equation to not include $k$ since we're looking for a system of equations to solve for $s$ and $t$ .

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