The question in the image is asking for the following:

(a) An angle measures $127^\circ$. What is the measure of its supplement?

(b) An angle measures $51^\circ$. What is the measure of its complement?

Solutions:

1. Supplementary Angles:

   • Supplementary angles add up to $180^\circ$.
   • To find the supplement of an angle, subtract the given angle from $180^\circ$.
   • For part (a): $180^\circ - 127^\circ = 53^\circ$.

   The measure of the supplement is $53^\circ$.

2. Complementary Angles:

   • Complementary angles add up to $90^\circ$.
   • To find the complement of an angle, subtract the given angle from $90^\circ$.
   • For part (b): $90^\circ - 51^\circ = 39^\circ$.

   The measure of the complement is $39^\circ$.

Would you like more details or have any questions? Here are 5 related questions for you:

1. What are the properties of complementary and supplementary angles?
2. Can two obtuse angles be supplementary? Why or why not?
3. How would you calculate the complement of an angle if the angle is greater than $90^\circ$?
4. Can two right angles be complementary?
5. How can supplementary and complementary angles be applied in geometry problems?

Tip: Remember, supplementary angles always add to $180^\circ$, while complementary angles add to $90^\circ$.