Question

ZG and ZH are complementary angles.
If mZG = (6x – 15)° and mZH = (3x + 6)°, find
mZH

Answer 1

Hey there! I'm happy to help!

Complementary angles add up to equal 90 degrees.

So, we can use and solve the following equation.

6x-15+3x+6=90

We combien like terms.

9x-9=90

We add 9 to both sides.

9x=99

We divide both sides by 9.

x=11

We plug this into the value for mZH.

3(11)+6

33+6

39

The measure of angle ZH is 39 degrees.

Have a wonderful day!

Answer 2

Angle ZH is 39 degrees.

Explanation:

Since ZG and ZH are complementary angles, this means that their sum is 90. In other words:

`\angle ZG+\angle ZH=90`

Substitute (6x-15) for ZG and (3x+6) for ZH. Thus:

`(6x-15)+(3x+6)=90`

Combine like terms:

`9x-9=90`

Add 9 to both sides:

`9x=99`

Divide both sides by 9:

`x=11`

So, the value of x is 11.

Now, substitute it back into the equation for ZH to find ZH:

`\angle ZH=3(11)+6`

Multiply:

`\angle ZH=33+6`

Add:

`\angle ZH=39`

And we're done!