To determine the measure of the third angle in the triangle, we can use the fact that the sum of all angles in a triangle is always $180^\circ$.

Given:

• First angle: $140^\circ$
• Second angle: $23^\circ$

Let's denote the third angle as $x$.

The equation we need to solve is: $140^\circ + 23^\circ + x = 180^\circ$

Now, solve for $x$:

$x = 180^\circ - (140^\circ + 23^\circ)$ $x = 180^\circ - 163^\circ = 17^\circ$

So, the measure of the third angle is $17^\circ$.

Would you like any further details or have any questions?

Here are some related questions you might find interesting:

1. How would you solve for an unknown angle in a triangle if only two angles are given?
2. What properties do all triangles share regarding their angles?
3. How would this problem change if the triangle was an isosceles or equilateral triangle?
4. Can a triangle have two angles larger than 90 degrees? Why or why not?
5. What would be the sum of the exterior angles of any triangle?

Tip: Always remember that the sum of the interior angles of any triangle is always $180^\circ$, which is a fundamental rule in geometry.