Two angles are complementary if the sum of their measures is 90°. The measure of the first angle is 5° less than 4 times the second angle. Put the measure of the FIRST angle in Blank 1 and the measure of the SECOND angle in Blank 2. Just write the number, do NOT write the word "degrees".
Let x = second angle, then 4x - 5 = first angle.
Therefore, x + 4x - 5 = 90
Solve for x.
To solve this problem, we need to create an equation based on the given information. Let's call the first angle "x" and the second angle "y".
From the problem, we know that two angles are complementary if their sum is 90°. So we can write the equation: x + y = 90.
Additionally, we are given that the first angle is 5° less than 4 times the second angle. This can be written as: x = 4y - 5.
Now we can solve the system of equations by substitution or elimination.
Substitution:
Using the second equation, we can substitute x in the first equation: 4y - 5 + y = 90.
Combining like terms: 5y - 5 = 90.
Adding 5 to both sides: 5y = 95.
Dividing both sides by 5: y = 19.
Therefore, the measure of the SECOND angle (Blank 2) is 19.
Substituting y = 19 into the second equation: x = 4(19) - 5.
Multiplying: x = 76 - 5.
Calculating: x = 71.
Therefore, the measure of the FIRST angle (Blank 1) is 71.
So, the first angle measures 71° and the second angle measures 19°.