Question

example #13: an angle measures three degrees less than twice the measure of its complement. find the measures of both angles.
a + c = 90
a = 2c - 3
2c - 3 + c = 90
3c = 93
c = 31
a + 31 = 90
a = 59

Explanation:

Step1: Set up the equations

Let the angle be $a$ and its complement be $c$. We know that $a + c=90$ (since complementary - angles add up to 90 degrees) and $a = 2c-3$.

Step2: Substitute $a$ into the first - equation

Substitute $a = 2c - 3$ into $a + c=90$. We get $(2c-3)+c = 90$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $2c-3 + c=3c-3$. So, $3c-3 = 90$.

Step4: Solve for $c$

Add 3 to both sides of the equation: $3c-3 + 3=90 + 3$, which gives $3c=93$. Then divide both sides by 3: $c=\frac{93}{3}=31$.

Step5: Solve for $a$

Substitute $c = 31$ into $a = 2c-3$. So, $a=2\times31 - 3=62 - 3=59$.

Answer:

The measures of the two angles are 59 degrees and 31 degrees.