In this problem, we need to determine the measures of angles 3 and 4 in the given triangle.

Solution

1. Sum of Angles in a Triangle: We know that the sum of angles in any triangle is always $180^\circ$.

2. Given Angles:

   • One angle is $47^\circ$.
   • Another angle is $48^\circ$.

3. Calculation of the Third Angle (Angle 3): Let angle 3 be the unknown angle, which we can find by using: $\text{Angle 3} = 180^\circ - 47^\circ - 48^\circ$ $= 180^\circ - 95^\circ$ $= 85^\circ$

   Therefore, the measure of angle 3 is 85°.

4. Measure of Angle 4: Since angle 4 is not inside the triangle but appears as an exterior angle adjacent to angle 47°, angle 4 can be calculated as the supplementary angle to angle 47° (since they form a straight line).

   $\text{Angle 4} = 180^\circ - 47^\circ$ $= 133^\circ$

   Thus, the measure of angle 4 is 133°.

Answers:

• The measure of angle 3 is 85°.
• The measure of angle 4 is 133°.

Would you like more details or have any questions?

Here are five related questions to further practice:

1. How do you calculate the interior angles of any triangle if two angles are known?
2. What are supplementary angles, and how do they relate to adjacent angles?
3. How can you verify that the sum of interior angles in a triangle is always $180^\circ$?
4. What is the difference between interior and exterior angles in polygons?
5. How can you find the measure of an exterior angle given two interior angles of a triangle?

Tip: Always remember that the sum of interior angles in a triangle is $180^\circ$, which is helpful in solving for unknown angles.