To find the measure of ∠1 in the triangle shown in the image, we can use the fact that the sum of the angles in a triangle is always 180°.

We are given two of the angles:

• One angle is 78°
• Another angle is 31°

Let's denote ∠1 as $x$.

Using the triangle sum property: $x + 78^\circ + 31^\circ = 180^\circ$

Now, we can solve for $x$: $x = 180^\circ - (78^\circ + 31^\circ)$ $x = 180^\circ - 109^\circ$ $x = 71^\circ$

So, the measure of ∠1 is 71°.

Let me know if you'd like further details or explanations!

Here are 5 related questions to expand on this:

1. How do you find the measure of an exterior angle of a triangle?
2. What happens to the sum of the angles if you extend one side of the triangle?
3. How does the Pythagorean theorem relate to right triangles?
4. Can the angles in a triangle be more than 90°? If so, what is that triangle called?
5. What is the definition of an acute, obtuse, and right triangle based on angles?

Tip: Always remember, the sum of the angles in any triangle adds up to 180°.