Two angles are complementary. The larger angle is $ 6^{\circ}$ less than five times the measure of the smaller

Question

Two angles are complementary. The larger angle is $ 6^{\circ}$ less than five times the measure of the smaller angle. What is the measure of the larger angle?

Examoogle · Accepted Answer

The correct answer is Option C: $74^\circ$. Use the options: Since the larger angle is $5 	imes 	ext{smaller} - 6$, adding 6 to each option should make the result divisible by 5. For 74, $74 + 6 = 80$, and $80/5 = 16$ (smaller angle). $74 + 16 = 90$, which satisfies the complementary condition.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the options: Since the larger angle is $5 	imes 	ext{smaller} - 6$, adding 6 to each option should make the result divisible by 5. For 74, $74 + 6 = 80$, and $80/5 = 16$ (smaller angle). $74 + 16 = 90$, which satisfies the complementary condition.

Formula Used: $$x + y = 90$$, $$y = 5x - 6$$

Given: Two angles are complementary, meaning their sum is 90 degrees. The larger angle is 6 degrees less than five times the smaller angle.

Steps: Define the variables: Let the smaller angle be $x$ and the larger angle be $y$. Since they are complementary, their sum is $90^\circ$.. Set up the second equation: According to the problem, the larger angle $y$ is 6 degrees less than five times the smaller angle $x$.. Substitute and solve for $x$: Substitute $y$ in the first equation: $x + (5x - 6) = 90$. Combining terms gives $6x - 6 = 90$, so $6x = 96$.. Calculate the larger angle $y$: Using the value of $x$, find $y$: $y = 90 - 16 = 74^\circ$. Alternatively, $y = 5(16) - 6 = 80 - 6 = 74^\circ$.

Answer: C is correct because the smaller angle is 16° and the larger angle is 74°, which sum to 90° and satisfy the given condition.

Exam Tip: This concept of complementary ($90^\circ$) and supplementary ($180^\circ$) angles frequently appears in Geometry and Trigonometry problems involving angle identities.

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)