Question

Find the value of the variable.

Answer 1

z = 19

Explanation:

These are complementary angles; both angles add up to 90°.

To solve this, we can combine like terms.

3z + (1)z + 14 = 90

3z + (1)z = 4z

**3z and z are the only pair of like terms.**

After combining like terms, we can proceed to solve this problem.

4z + 14 = 90.

Since there is an addition sign in front of 14, we do the opposite, subtraction.

First, subtract 14 from 90 and 14.

4z + 14 = 90

- 14 - 14

------------------

4z = 76

**ELIMINATE 14.**

Lastly, divide 76 from 4; this is because 4 is the coefficient.

4x = 76

76 ÷ 4 = 19

Therefore, z = 19.

Answer 2

When you add all of these angles, the sum should be 180°. This helps us to figure out the value of the variable.

Now, you must create an equation.

3z+14+z+90=180

4z+14+90=180

4z+104=180

4z+104-104=180-104

4z=76

z=19

∴The value of the variable is 19.

To check:

3(19)+14+19+90

57+14+19+90

90+90

180

All of the angles together have a sum of 180 degrees, meaning that our value for the variable is indeed correct.

Hope this helps.