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

Given:

• First angle = $73^\circ$
• Second angle = $17^\circ$

Let the third angle be $x$.

Then, $73^\circ + 17^\circ + x = 180^\circ$

Adding $73^\circ$ and $17^\circ$: $90^\circ + x = 180^\circ$

Now, subtract $90^\circ$ from both sides to solve for $x$: $x = 180^\circ - 90^\circ = 90^\circ$

The measure of the third angle is $90^\circ$.

Would you like further details or have any questions?

Here are five related questions to explore further:

1. What are the properties of a right triangle, since one angle here is $90^\circ$?
2. How can you use trigonometric ratios in a right triangle?
3. How do you classify triangles based on their angles and sides?
4. What is the significance of the angle sum property in different polygons?
5. How would the calculations differ if the triangle were non-Euclidean?

Tip: Always remember the angle sum property of triangles, as it is fundamental in both geometry and trigonometry.