Answer:
The measures are 22 and 68 degrees
Step-by-step explanation:
for a right triangle, the total angle measure gives 90
Let one of the acute angle be x and the other be y
The measure of one of the acute angle is 4 times the the difference of the measure of the other angle and 5
x = 4(y-5)
Also x + y = 90
Put i into ii
4(y-5) + y = 90
4y-20 + y = 90
5y-20 = 90
5y = 90 + 20
5y = 110
y = 110/5
y = 22
But;
x = 4(y-5)
x = 4(22-5)
x = 4(17)
x = 68
The sum of the acute angles in a right-angled triangle is 90.
The acute angles are 22 and 68 degrees
Let the acute angles be x and y, such that:
[tex]\mathbf{y = 4(x - 5)}[/tex]
So, we have:
[tex]\mathbf{x + y = 90}[/tex]
Substitute 4(x - 5) for y
[tex]\mathbf{x + 4(x - 5) = 90}[/tex]
Open brackets
[tex]\mathbf{x + 4x - 20 = 90}[/tex]
Add x and 4x
[tex]\mathbf{5x - 20 = 90}[/tex]
Add 20 to both sides
[tex]\mathbf{5x = 110}[/tex]
Divide both sides by 5
[tex]\mathbf{x = 22}[/tex]
Recall that:
[tex]\mathbf{y = 4(x - 5)}[/tex]
So, we have:
[tex]\mathbf{y = 4(22 - 5)}[/tex]
[tex]\mathbf{y = 68}[/tex]
Hence, the acute angles are 22 and 68 degrees
Read more about acute angles at:
https://brainly.com/question/10388714
