Question

question 3 of 13, step 1 of 1
two angles are complementary if the sum of their measures is 90°. find two complementary angles such that one of the angles is 147 less than 2 times the other angle. (round to two decimal places if necessary.)
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° the smaller complementary angle
° the larger complementary angle
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Explanation:

Step1: Set up the equation

Let one angle be $x$ and the other be $y$. We know that $x + y=90$ (complementary angles) and $y = 2x-14$. Substitute $y$ into the first - equation: $x+(2x - 14)=90$.

Step2: Simplify the equation

Combine like - terms: $x+2x-14 = 90$. This gives $3x-14 = 90$.

Step3: Solve for $x$

Add 14 to both sides of the equation: $3x=90 + 14$, so $3x=104$. Then divide both sides by 3: $x=\frac{104}{3}\approx34.67$.

Step4: Solve for $y$

Substitute $x=\frac{104}{3}$ into $y = 90 - x$. So $y=90-\frac{104}{3}=\frac{270 - 104}{3}=\frac{166}{3}\approx55.33$.

Answer:

The smaller complementary angle: $34.67^{\circ}$
The larger complementary angle: $55.33^{\circ}$