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Anit [1.1K]
3 years ago
14

In triangle MNO, angle N is 5 times the measure of angle M, and angle O is 4 times the measure of angle M

Mathematics
1 answer:
Helen [10]3 years ago
4 0

Answer:

m\angle M=18\°\\\\m\angle N=90\°\\\\m\angle O=72\°

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:

M+N+O=180    [Equation 1]

Based on the information given in the exercise, you know that:

N=5M    [Equation 2]

O=4M    [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:

M+5M+4M=180\\\\10M=180\\\\M=\frac{180}{10}\\\\M=18

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:

N=5(18)=90\\\\\\O=4(18)=72

Therefore:

m\angle M=18\°\\\\m\angle N=90\°\\\\m\angle O=72\°

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