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Answer :
Final answer:
Using a system of equations, the measures of the two supplementary angles have been calculated: one measures 107.9 degrees and the other measures 72.1 degrees.
Explanation:
An angle that is supplementary to another angle has a sum of 180 degrees with that angle. Let's name the first angle A and its supplementary angle B.
Given that A is 35.8 degrees more than B, we can set up the following equation to represent their relationship:
A = B + 35.8 degrees.
Together, they must add up to 180 degrees, so we also have the equation: A + B = 180 degrees.
By substituting the first equation into the second, we can solve for B: (B + 35.8) + B = 180, which simplifies to 2B + 35.8 = 180.
Solving for B yields B = 72.1 degrees.
Now that we know B, we can find A by adding 35.8 degrees to B, giving us A = 107.9 degrees.
Therefore, the two angles are 107.9 degrees and 72.1 degrees.
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