Two angles are complementary. The measure of the larger angle is 5 more than 4 times the measure of the smaller angle.

Large Angle = 73°

Small Angle = 17°

Step-by-step 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°.

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step-by-step explanation:

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