M∠GHI = 3x° and m∠LMN = 17x°. If ∠GHI and ∠LMN are supplementary, find the measure of each angle.

Mathematics

2 answers:

Savatey [412]3 years ago

3 0

If they are supplementary then 3x + 17x = 180

20x = 180

x = 9
m<GHI = 27 degrees
m < LMN = 153 degrees

Helga [31]3 years ago

3 0

Answer:

The answers are:

m∠GHI=27

m∠LMN=153

Step-by-step explanation:

In order to determine the answer, we have to know about supplementary angles.

Two angles are supplementary when the sum of them is 180 degrees.

So, with this information, we can build an equation. This equation will be useful to determine the value of "x" variable. Then, with this value, we will determine the value of each angle.

m∠GHI+m∠LMN=3x+17x=180

$3x+17x=180\\20x=180\\x=\frac{180}{20}\\ \\x=9$

Then, we can determine each angle:

m∠GHI=3*9=27

m∠LMN=17*9=153

Finally, the measure of each angle is:

m∠GHI=27

m∠LMN=153

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Serggg [28]

Answer:

the second option

Step-by-step explanation:

in ax²+bx+c = 0:

$x = \frac{-b+-\sqrt{b^2-4ac} }{2a}$

subtract both sides by 6 to get to this form, as the right side will be left with 0

6x² + 8x - 6 = 0

here, the coefficient for x² (a) is 6, the coefficient for x (b) is 8, and the remaining number added on (c) is -6

plugging our numbers into the formula, we get

$x = \frac{-8+-\sqrt{(-8)^2-4(6)(-6)} }{2(6)}\\= \frac{-8+-\sqrt{64-(-144)} }{12} \\= \frac{-8+-\sqrt{208} }{12} \\ = \frac{-8+\sqrt{208} }{12} or \frac{-8-\sqrt{208} }{12}\\= 0.53518375848 or -1.86851709182\\= approximately -1.87, 0.54$