To find the measure of angle 1 in this triangle, we can use the fact that the sum of the interior angles in any triangle is always 180°.

The given angles in the triangle are:

• 117°
• 33°

Let angle 1 be represented by $\angle 1$.

Now, using the sum of angles in a triangle: $\angle 1 + 117^\circ + 33^\circ = 180^\circ$

Let's solve for $\angle 1$: $\angle 1 = 180^\circ - 117^\circ - 33^\circ$ $\angle 1 = 180^\circ - 150^\circ = 30^\circ$

Therefore, the measure of $\angle 1$ is 30°.

Would you like further details or have any questions?

Here are some related questions to consider:

1. How do you prove the sum of the interior angles of a triangle is always 180°?
2. What is the exterior angle theorem, and how does it apply to this triangle?
3. How can you find missing angles in other polygons, such as quadrilaterals or pentagons?
4. What happens if a triangle has an angle greater than 180°? Is it still a triangle?
5. Can you calculate angles in non-Euclidean geometry, where the sum of angles in a triangle is not always 180°?

Tip: Always remember that the sum of angles in a triangle is constant (180°) in Euclidean geometry, regardless of the type of triangle (acute, obtuse, or right).