Let us solve problem 28. The triangle provided has two angles and a missing angle $x^\circ$. To find $x$, we use the Triangle Sum Theorem, which states:

$\text{Sum of all angles in a triangle} = 180^\circ.$

Given:

• One angle is $102^\circ$,
• Another angle is $8^\circ$,
• Missing angle $x$.

Steps:

1. Add the two known angles: $102^\circ + 8^\circ = 110^\circ.$

2. Subtract their sum from $180^\circ$: $x = 180^\circ - 110^\circ = 70^\circ.$

Final Answer:

The missing angle $x = 70^\circ$.

Would you like more clarification or details about the process?

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Related Questions:

1. How does the Triangle Sum Theorem apply to different types of triangles?
2. Can the sum of the angles in any polygon be calculated similarly?
3. What are some other methods to find missing angles in triangles?
4. How can exterior angles help verify this calculation?
5. What happens if two angles in a triangle are equal?

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Tip:

Always double-check your calculations to ensure the sum of all angles equals $180^\circ$.