The measure of an angle is 6 less than 5 times its complement. What is the measure of the complement?

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pierretteA · Accepted Answer

Two angles are complementary if the sum of their measures is 90∘. If x is the measure of the angle, then 90−x is the measure of the complement, both in degrees. Using the given statement, we can write: x=5(90−x)−6 Solve for x: x=450−5x−6 x=444−5x 6x=444 x=74 So, the measure of the complement is 90−74=16∘.

fudzisako · Accepted Answer

Step 1: Let&#039;s assume the measure of the angle is x.According to the problem statement, the measure of an angle is 6 less than 5 times its complement. The complement of an angle is the angle that, when added to the given angle, results in a right angle (90 degrees). The complement of x can be represented as 90−x.Given that the measure of the angle is 6 less than 5 times its complement, we can write the equation as:x=5(90−x)−6To solve this equation, let&#039;s simplify it:x=450−5x−6Step 2: Now, let&#039;s gather like terms:x+5x=450−66x=444To isolate x, we divide both sides of the equation by 6:6x6=4446x=74Therefore, the measure of the angle is 74 degrees.Step 3: To find the measure of the complement, we substitute x back into the expression for the complement:Complement =90−x=90−74=16Hence, the measure of the complement is 16 degrees.To summarize, the measure of the angle is 74 degrees, and the measure of its complement is 16 degrees.

xleb123 · Accepted Answer

Answer:x+65Explanation:According to the given information, we have the equation:x=5y−6To find the measure of the complement, we need to solve for y. Rearranging the equation, we get:5y=x+6Dividing both sides by 5, we have:y=x+65Therefore, the measure of the complement is x+65.

Jazz Frenia · Accepted Answer

According to the problem, we can set up the following equation:x=5(90∘−x)−6To solve this equation, we&#039;ll start by distributing the 5:x=450∘−5x−6Next, we&#039;ll combine like terms:x+5x=450∘−66x=444∘Finally, we&#039;ll solve for x by dividing both sides of the equation by 6:x=444∘6x=74∘Therefore, the measure of the angle is 74∘.To find the measure of its complement, we substitute the value of x back into the equation for the complement:Complement =90∘−x=90∘−74∘Complement =16∘Hence, the measure of the complement is 16∘.

The measure of an angle is 6 less than 5 times its complement. What is the measure of the complement?

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