Question

1. in triangle mno, ∠n is 5 times the measure of ∠m, and ∠o is 4 times the measure of ∠m.

∠m =
∠n =
∠o =

Explanation:

Step1: Define variable for $\angle M$

Let $m\angle M = x$

Step2: Express other angles in $x$

$m\angle N = 5x$, $m\angle O = 4x$

Step3: Sum angles to $180^\circ$

$$x + 5x + 4x = 180^\circ$$

Step4: Solve for $x$

$$10x = 180^\circ \implies x = \frac{180^\circ}{10} = 18^\circ$$

Step5: Calculate each angle

$m\angle M = 18^\circ$, $m\angle N = 5\times18^\circ=90^\circ$, $m\angle O = 4\times18^\circ=72^\circ$

Answer:

$\angle M = 18^\circ$
$\angle N = 90^\circ$
$\angle O = 72^\circ$