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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