Answer:
[tex]m\angle M=18\°\\\\m\angle N=90\°\\\\m\angle O=72\°[/tex]
Step-by-step explanation:
In order to find the measure of each angle, it is important to remember that the sum of the interior angles of a triangle is 180 degrees. Knowing this, you can write the following equation:
[tex]M+N+O=180[/tex] [Equation 1]
Based on the information given in the exercise, you know that:
[tex]N=5M[/tex] [Equation 2]
[tex]O=4M[/tex] [Equation 3]
Then, you can substitute the Equations 2 and 3 into the Equation 1 and then solve for "M" in order to find the measure of the angle "M" in degrees:
[tex]M+5M+4M=180\\\\10M=180\\\\M=\frac{180}{10}\\\\M=18[/tex]
Substituting this value into the Equations 2 and 3, you can find the measure of the angle "N" in degrees and the mesure of the angle "O" in degrees. These are:
[tex]N=5(18)=90\\\\\\O=4(18)=72[/tex]
Therefore:
[tex]m\angle M=18\°\\\\m\angle N=90\°\\\\m\angle O=72\°[/tex]
The angles are mathematically given as
M = 18 degrees
N = 90 degrees
O = 72 degrees
Generally the equation for the angle sum of a triangle is mathematically given as
180 = 5M + M + 4M
180 = 10M
M = 18 degrees
Therefore
N = 5(18)
N= 90 degrees
Hence
O = 4(18)
O= 72 degrees
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