Question

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

Answer 1

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:

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