the measures of two complementary angles are 16z-9 and 4z+3. Find the measures of the angles.

Two Angles are Complementary if they add up to 90 °

In this case :

16 z - 9 ° + 4 z + 3 ° = 90 °

20 z - 6 ° = 90 ° Add 6 ° to both sides

20 z - 6 ° + 6 ° = 90 ° + 6 °

20 z = 96 ° Divide both sides by 20

z = 96 ° / 20 = 4.8 ° = 4 ° 48 ´

16 z - 9 ° = 16 * 4.8 ° - 9 ° = 76.8 ° - 9 ° = 67.8 ° = 67 ° 48 ´

4 z + 3 ° = 4 * 4.8 ° + 3 ° = 19.2 ° + 3 ° = 22. 2 ° = 22 ° 12 ´

Well, isn't that just the perfect setup for some mathematical comedy! Two complementary angles, working together to create a right angle. Let's find their measures and make sure they're in harmony!

We have two angles: 16z - 9 and 4z + 3. Since they're complementary, they add up to 90 degrees. So, we can set up an equation: (16z - 9) + (4z + 3) = 90.

Now, let's gather all the terms on one side: 16z + 4z - 9 + 3 = 90. Simplify that and we get: 20z - 6 = 90.

Time to bring in some circus math skills! Let's solve for z. We add 6 to both sides: 20z = 96. Divide both sides by 20, and we get z = 4.8.

With z in hand, we can substitute it back into our angles:

First angle: 16(4.8) - 9 = 76.8 - 9 = 67.8 degrees.

Second angle: 4(4.8) + 3 = 19.2 + 3 = 22.2 degrees.

And there you have it! The first angle is 67.8 degrees, and the second angle is 22.2 degrees. They may be complementary, but their comedic timing is always spot on!

To find the measures of the angles, we need to set up an equation using the fact that the sum of two complementary angles is equal to 90 degrees.

Let the first angle be represented by 16z-9, and the second angle be represented by 4z+3.

The equation is: (16z-9) + (4z+3) = 90

Simplifying the equation, we get: 20z - 6 = 90

Adding 6 to both sides of the equation, we get: 20z = 96

Dividing both sides of the equation by 20, we get: z = 4.8

Now, we can substitute the value of z back into the given expressions for the angles.

The first angle = 16z-9 = 16(4.8)-9 = 76.8-9 = 67.8 degrees

The second angle = 4z+3 = 4(4.8)+3 = 19.2+3 = 22.2 degrees

Therefore, the measures of the angles are 67.8 degrees and 22.2 degrees.

To find the measures of the angles, we need to set up an equation using the fact that complementary angles add up to 90 degrees.

Given that the measures of the angles are 16z-9 and 4z+3, we can set up the following equation:

(16z-9) + (4z+3) = 90

Simplifying the equation:

20z - 6 = 90

Adding 6 to both sides:

20z = 96

Dividing by 20:

z = 96/20

Simplifying:

z = 4.8

Now that we have the value of z, we can substitute it back into the expressions for the angle measures to find their actual values.

For the first angle:

16z-9 = 16(4.8)-9 = 76.8 - 9 = 67.8 degrees

For the second angle:

4z+3 = 4(4.8)+3 = 19.2 + 3 = 22.2 degrees

Therefore, the measures of the two angles are 67.8 degrees and 22.2 degrees.