An angle measures 7.4° more than the measure of its complementary angle. What is the measure of each angle?
The Correct Answer and Explanation is :
The correct answer is: ( 48.7^\circ ) and ( 41.3^\circ )
To find the measures of the two complementary angles, we can set up an equation based on the information provided. Let’s denote the measure of one angle as ( x ). The complementary angle, which is ( 90^\circ – x ), is given to be ( 7.4^\circ ) less than the first angle. Therefore, we can express this relationship mathematically as follows:
[
x = (90^\circ – x) + 7.4^\circ
]
Now, we can simplify this equation. Start by distributing and rearranging the terms:
[
x = 90^\circ – x + 7.4^\circ
]
Combine like terms:
[
x + x = 90^\circ + 7.4^\circ
]
[
2x = 97.4^\circ
]
Next, divide both sides by 2 to find ( x ):
[
x = \frac{97.4^\circ}{2} = 48.7^\circ
]
Now that we have the measure of the first angle, we can find the complementary angle:
[
90^\circ – x = 90^\circ – 48.7^\circ = 41.3^\circ
]
So, the two angles are ( 48.7^\circ ) and ( 41.3^\circ ).
Explanation:
The concept of complementary angles refers to two angles that add up to ( 90^\circ ). The problem states that one angle is ( 7.4^\circ ) more than its complementary counterpart. By defining the first angle as ( x ) and recognizing that the second angle can be expressed as ( 90^\circ – x ), we can create a solvable equation.
By rearranging and combining the terms, we isolate ( x ) and find its measure. The steps involve basic algebraic manipulation, reinforcing the relationships between angles and providing a clear method for solving problems involving complementary angles. The final result shows that the two angles not only meet the criteria of being complementary, but also accurately reflect the specified difference of ( 7.4^\circ ).