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ChopinTheChicken

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!

xKelvin

Answer:

Angle ZH is 39 degrees.

Step-by-step explanation:

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

[tex]\angle ZG+\angle ZH=90[/tex]

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

[tex](6x-15)+(3x+6)=90[/tex]

Combine like terms:

[tex]9x-9=90[/tex]

Add 9 to both sides:

[tex]9x=99[/tex]

Divide both sides by 9:

[tex]x=11[/tex]

So, the value of x is 11.

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

[tex]\angle ZH=3(11)+6[/tex]

Multiply:

[tex]\angle ZH=33+6[/tex]

Add:

[tex]\angle ZH=39[/tex]

And we're done!

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