Finding the Unknown Angle Measure in a Triangle and Validity of Given Interior Angles in a Triangle

To find the unknown angle measure in a triangle, recall that the sum of the interior angles in any triangle is always 180 degrees.

1. Sum of Angles: If you have two angles (23° and 71°), you can find the third angle (let’s call it x) using the equation:

[

23° + 71° + x = 180°

]
2. Combine Known Angles: Add the known angles together:

[

23° + 71° = 94°

]
3. Solve for x: Now, substitute back into the equation:

[

94° + x = 180°

]

Subtract 94° from both sides:

[

x = 180° – 94° = 86°

]

So, the unknown angle measure is 86°.

Now, regarding the second part of your question, we need to check if a triangle can have interior angles of 23°, 71°, and 96°.

1. Check Sum of Angles: Add these angles together:

[

23° + 71° + 96° = 190°

]
2. Conclusion: Since the sum (190°) is greater than 180°, a triangle cannot have angles measuring 23°, 71°, and 96°.