Answer:
Large Angle = 73°
Small Angle = 17°
Explanation:
Set up equations:
90 = x + y
Where x is the larger angle and y is the smaller angle
(The sum of these angle is 90 degrees because they are complementary)
x = 5 + 4y
Where x is the larger angle and y is the smaller angle
Make the equation equal to x:
90 = x + y
Subtract y on both sides:
90 = x + y
-y -y
90 - y = x
Now, we can set the two equations equal to each other.
x = 5 + 4y
90 - y = x
5 + 4y = 90 - y
Add y on both sides:
5 + 4y = 90 - y
+y +y
5 + 5y = 90
Subtract 5 on both sides:
5 + 5y = 90
-5 -5
5y = 85
Divide by 5 on both sides:
5y = 85
/5 /5
y = 17
Therefore, the smaller angle measures 17°.
We can substitute this angle measure into one of the equations to find the value of x. Let's use 90 - y = x.
Substitute:
90 - y = x
90 - 17 = x
Subtract:
73 = x
Therefore, the measure of the larger angle is 73°.