Question

solve for m

Explanation:

Step1: Find angle $n$ (triangle sum)

The sum of angles in a triangle is $180^\circ$.
$$n = 180^\circ - 61^\circ - 87^\circ = 32^\circ$$

Step2: Find $m$ (supplementary angle)

$m$ and $61^\circ$ are supplementary? No, $m$ is an exterior angle equal to the sum of remote interior angles:
$$m = 87^\circ + n = 87^\circ + 32^\circ$$
Or use linear pair: $m + 61^\circ = 180^\circ$ is wrong; correct: exterior angle theorem: $m = 87^\circ + 32^\circ = 119^\circ$
(Alternative: $m = 180^\circ - (180^\circ - 61^\circ - 87^\circ) - 61^\circ$ simplifies to same)

Answer:

$119^\circ$