<a and <d are complemetary . <a and <e are supplementary what can you conclude about <d & <e? explain yr answer. what type of reasoning inductive or deductive, do you use when solving this problem?

<d is always less than <e.

explain to me how? and its deductive or inductive

To determine what can be concluded about <d and <e when <a and <d are complementary, and <a and <e are supplementary, we need to understand the relationships between these angles.

Complementary angles are two angles that add up to 90 degrees, while supplementary angles are two angles that add up to 180 degrees.

Given that <a and <d are complementary, we can deduce that:

<d + <a = 90 degrees

On the other hand, <a and <e are supplementary, which leads us to the conclusion that:

<a + <e = 180 degrees

Now, let's rearrange the first equation to solve for <d:

<d = 90 - <a

Substituting this value into the second equation, we have:

(90 - <a) + <e = 180

Rearranging this equation further, we find:

<e = 180 - (90 - <a)
<e = 90 + <a

Based on these equations, we can conclude that <d and <e are also complementary angles, since <e = 90 + <a, and <d = 90 - <a. Therefore, the conclusion is that <d and <e are complementary angles.

Regarding the type of reasoning used in solving this problem, we made deductions based on the definitions and properties of complementary and supplementary angles. This is an example of deductive reasoning, where we apply logical rules and facts to reach specific conclusions.