Angles a and b are complementary angles. Veronica knows that angle a is less than 50 degrees. What is the measure of angle b?
Understand the Problem
The question involves finding the measure of angle b given that angles a and b are complementary, meaning their measures add up to 90 degrees. Since angle a is less than 50 degrees, we need to determine the maximum possible value for angle b.
Answer
The maximum measure of angle \( b \) is \( 40^\circ \).
Answer for screen readers
The measure of angle ( b ) can be at most ( 40^\circ ).
Steps to Solve
- Understanding Complementary Angles
Complementary angles are two angles whose measures add up to 90 degrees.
This means we can express their relationship mathematically as: $$ a + b = 90^\circ $$
- Substituting the given value
Since we know that angle $a$ is less than 50 degrees, we can express this as: $$ a < 50^\circ $$
- Finding the maximum value for angle b
To find the maximum possible value for angle $b$, substitute the largest possible value for $a$ into the complementary angle equation: $$ b = 90^\circ - a $$
Since $a$ can be less than 50 degrees, the largest possible value of $a$ would be just under 50. Therefore, we can plug this into our equation: $$ b = 90^\circ - 50^\circ = 40^\circ $$
Since $b$ increases as $a$ decreases, we conclude that the maximum possible value for $b$ occurs when $a$ is just under 50 degrees.
- Concluding the maximum measure of b
Thus, the maximum possible value for angle $b$ is: $$ b < 40^\circ $$
The measure of angle ( b ) can be at most ( 40^\circ ).
More Information
Angle ( b ) is the remaining angle needed to reach a total of ( 90^\circ ) when angle ( a ) is less than ( 50^\circ ). This problem highlights how angles can be interrelated using the concept of complementary angles.
Tips
- Assuming that ( a ) can equal ( 50^\circ ). Remember that ( a ) must be less than ( 50^\circ ), which means ( b ) has to be more than ( 40^\circ ).
- Forgetting to express the relationship properly may lead to incorrect calculations.
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