The given image shows a triangle with two known angles, 54° and 32°. The task is to find the measure of the missing angle, which is labeled as $m \angle 1$.

In a triangle, the sum of all interior angles is always 180°. Therefore, we can use this fact to find $m \angle 1$.

Let $m \angle 1$ represent the unknown angle.

$m \angle 1 + 54^\circ + 32^\circ = 180^\circ$

Simplifying:

$m \angle 1 = 180^\circ - 54^\circ - 32^\circ$

$m \angle 1 = 180^\circ - 86^\circ = 94^\circ$

Thus, the measure of $m \angle 1$ is:

$m \angle 1 = 94^\circ$

Would you like more details or have any other questions?

Here are five related questions:

1. How can we prove the sum of angles in any triangle is 180°?
2. What is an exterior angle of a triangle, and how is it related to interior angles?
3. Can a triangle have more than one obtuse angle? Why or why not?
4. What is the difference between acute, obtuse, and right angles in a triangle?
5. How can you find missing angles in other polygons?

Tip: Always remember that the sum of the interior angles in any polygon can be calculated using the formula $(n - 2) \times 180^\circ$, where $n$ is the number of sides of the polygon.