the measure 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 ° (a Right Angle).

Or :

A + B = 90 °

In this case :

A = 16 z - 9 °

B = 4 z + 3 °

A + B = 90 °

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

20 z / 20 = 96 ° / 20

z = 4.8 ° = 4 ° 48 ´

A = 16 z - 9 °

A = 16 * 4.8 ° - 9 ° =

76.8 ° - 9 ° =

67.8 ° = 67 ° 48 ´

B = 4 z + 3 ° =

4 * 4.8 ° + 3 ° =

19.2 ° + 3 ° = 22.2 ° = 22 ° 12 ´

Solution :

A = 67.8 ° = 67 ° 48 ´

B = 22.2 ° = 22 ° 12 ´

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

Let's set up the equation:

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

Now, let's solve the equation:

Combine the like terms:

16z + 4z - 9 + 3 = 90

20z - 6 = 90

Add 6 to both sides of the equation:

20z = 96

Divide both sides by 20:

z = 4.8

Now that we have the value of z, we can substitute it back into the expressions for the angles to find their measures:

Angle 1 = 16z - 9 = 16(4.8) - 9 = 76.8 - 9 = 67.8 degrees

Angle 2 = 4z + 3 = 4(4.8) + 3 = 19.2 + 3 = 22.2 degrees

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

To find the measures of the two complementary angles, we need to set up an equation based on the definition of complementary angles.

Complementary angles are two angles whose sum is equal to 90 degrees.

Let's set up the equation:

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

Now, we can solve this equation to find the value of z and then substitute it back into the expressions to find the measures of the angles.

Simplifying the equation:

20z - 6 = 90

Adding 6 to both sides:

20z = 96

Dividing both sides by 20:

z = 4.8

Now, substitute the value of z back into the expressions for the angles:

First angle:

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

Second angle:

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

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