Question

Two angles are complementary. The measure of the larger angle is 10 more than 4 times the measure of the small angle. Find the measures of both angles.

Answer 1

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 2

Answer:

$a=16$

$b=74$

Step-by-step explanation:

If two angles are complementary to each other, then their sum is 90 degrees.

So we have: $a+b=90$.

Let's say $b$ is the larger of the two.

We have that $b$ is 10 more than 4 times the measure of $a$.

An equation this is: $b=10+4a$.

So I'm going to plug second equation into first equation:

$a+b=90$ with $b=10+4a$:

$a+(10+4a)=90$

Combine like terms:

$5a+10=90$

Subtract 10 on both sides:

$5a=80$

Divide both sides by 5:

$a=\frac{80}{5}$

Simplify:

$a=16$

Now to find $b$:

$b=10+4a$ with $a=16$:

$b=10+4(16)$

$b=10+64$

$b=74$