Question

a. determine the measure of an angle whose measure is 5 times that of its complement. b. if two angles of a triangle are complementary, what is the measure of the third angle? a. the angle measures □°

Explanation:

Part a

Step1: Define variables

Let the measure of the complement angle be $x$ degrees. Then the angle we want to find is $5x$ degrees.

Step2: Use complementary angle property

Complementary angles add up to $90^\circ$. So, $x + 5x = 90$.

Step3: Solve the equation

Combine like terms: $6x = 90$. Then divide both sides by 6: $x=\frac{90}{6}=15$.

Step4: Find the angle

The angle is $5x$, so substitute $x = 15$: $5\times15 = 75$.

Step1: Recall triangle angle sum

The sum of the interior angles of a triangle is $180^\circ$.

Step2: Use complementary angles

If two angles are complementary, their sum is $90^\circ$. Let the third angle be $y$. Then $90 + y = 180$.

Step3: Solve for $y$

Subtract 90 from both sides: $y = 180 - 90 = 90$.

Answer:

$75$

Part b