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An angle measures $120.6^\circ$ less than the measure of its supplementary angle. What is the measure of each angle?

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Complementary and supplementary angles

Full solution

Q. An angle measures

120.6^\circ

less than the measure of its supplementary angle. What is the measure of each angle?

Define Angles: Let's denote the smaller angle as $A$ and its supplementary angle as $B$ . We know that the sum of supplementary angles is $180°$ . The problem states that angle $A$ is $120.6°$ less than angle $B$ . We can set up the following equation: $\newline$ $A + B = 180°$ (since they are supplementary angles) $\newline$ $A = B - 120.6°$ (since $A$ is $120.6°$ less than $B$ )
Set Up Equation: Now we can substitute the expression for $A$ into the first equation: $(B - 120.6°) + B = 180°$
Solve for B: Combine like terms to solve for B: $\newline$ $2B - 120.6° = 180°$ $\newline$ $2B = 180° + 120.6°$ $\newline$ $2B = 300.6°$
Find Angle B: Divide both sides by $2$ to find the measure of angle B: $\newline$ $B = 300.6° \div 2$ $\newline$ $B = 150.3°$
Find Angle A: Now that we have the measure of angle B, we can find the measure of angle A by subtracting $120.6^\circ$ from B: $\newline$ $A = B - 120.6^\circ$ $\newline$ $A = 150.3^\circ - 120.6^\circ$ $\newline$ $A = 29.7^\circ$

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