Answer:
Step-by-step explanation:
Let the measurement of the smaller angle = x
Larger angle = 4x + 10
x + (4x + 10) = 90 {complementry}
5x + 10 = 90
5x = 90 -10
5x = 80
x = 80/5
x = 16
Smaller angle = 16
Larger angle = 4*16 + 10 = 64+10 = 74
Answer:
[tex]a=16[/tex]
[tex]b=74[/tex]
Step-by-step explanation:
If two angles are complementary to each other, then their sum is 90 degrees.
So we have: [tex]a+b=90[/tex].
Let's say [tex]b[/tex] is the larger of the two.
We have that [tex]b[/tex] is 10 more than 4 times the measure of [tex]a[/tex].
An equation this is: [tex]b=10+4a[/tex].
So I'm going to plug second equation into first equation:
[tex]a+b=90[/tex] with [tex]b=10+4a[/tex]:
[tex]a+(10+4a)=90[/tex]
Combine like terms:
[tex]5a+10=90[/tex]
Subtract 10 on both sides:
[tex]5a=80[/tex]
Divide both sides by 5:
[tex]a=\frac{80}{5}[/tex]
Simplify:
[tex]a=16[/tex]
Now to find [tex]b[/tex]:
[tex]b=10+4a[/tex] with [tex]a=16[/tex]:
[tex]b=10+4(16)[/tex]
[tex]b=10+64[/tex]
[tex]b=74[/tex]
