Mathematics, 06.09.2020 02:01 ziyonsolange

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

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Answer from: tbixler2021

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

The measure of angle ZH is 39 degrees.

Have a wonderful day!

Answer from: MathChic68

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:

$\angle ZG+\angle ZH=90$

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!

Answer from: Quest

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Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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

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