The image shows a triangle with angles labeled 46° and 49°. We need to find the measure of angles 3 and 4.

Step-by-step solution:

1. Understanding the problem:

   • The sum of the interior angles of a triangle is always 180°.
   • Two angles of the triangle are given as 46° and 49°.

2. Finding the third angle (angle 3):

   • The measure of the third angle can be found by subtracting the sum of the other two angles from 180°: $\text{Angle 3} = 180^\circ - 46^\circ - 49^\circ$ $\text{Angle 3} = 180^\circ - 95^\circ = 85^\circ$

Thus, the measure of angle 3 is 85°.

Would you like further details or to ask additional questions?

Follow-up Questions:

1. What are the basic properties of a triangle's angles?
2. How can we check if a triangle is valid based on its angles?
3. What happens if the sum of the angles is not 180° in a polygon?
4. Can you calculate the angles of an obtuse triangle?
5. How do the angles affect the type of triangle (scalene, isosceles, etc.)?

Tip:

Always remember that the sum of interior angles in any triangle is 180°, and this rule can help solve for unknown angles!