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Contact [7]
3 years ago
9

Two angles are complementary. the measure of one angle is 6° more than one-half of the measure of the other. find the measure of

each angle.
Mathematics
2 answers:
expeople1 [14]3 years ago
7 0
First, write an equation system based on the problem
We could write "two angels are complementary" as
⇒ a + b = 90° (1st equation)
We could write "<span>the measure of one angle is 6° more than one-half of the measure of the other" as
</span>⇒ a = 6° + \frac{1}{2}b (2nd equation)
<span>
Second, solve the equation system by substituting a from the second equation to the first equation
a + b = 90</span>°
6° + \frac{1}{2}b + b = 90°
6° + \frac{3}{2}b = 90°
\frac{3}{2}b = 84°
b = 84° × \frac{2}{3}
b = 56°

Substitute the measurement of b
a + b = 90°
a + 56° = 90°
a = 90° - 56°
a = 34°

The answer are 56° and 34°
Sidana [21]3 years ago
6 0
Complementary angles total 90°
One angle is 6 + .5x, so both angles added together is
x + (6 +  0.5 x) = 90 \\  1.5x  + 6 = 90 \\ 1.5x = 84 \\ x = 56 \\ 90 - 56 = 34
First, we add one angle to the other, and set it to 90°. Then, we simplify the equation. Then, we subtract 6 from both sides. Then we divide both sides by 1.5
The first angle is 56°
The second angle is 90 - 56, which is 34°
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