How do you prove angles are supplementary?

Answer 1

You must prove that the sum of both angles is equal to 180 degrees. ("If two angles form a linear pair, then they are supplementary; that is, the sum of their measures is 180 degrees.")

A good way to start is to look at your geometric theorems and think about if you could use any to determine the measurement of your angles.

A few ways to consider include:

a) Determine the measurement of #/_ ##ABC# and the measurement of #/_ ##ABD#, and prove that the combined measurements#=180# degrees.

b) Determine that the measurement of #/_CBD=180# degrees. If you choose this method, you can use the linear pairs postulate to prove that since the measure of #/_CBD=180# degrees, the angles that are added to form this angle (#/_ABC# and #/_ABD#) must be supplementary.

You can find a comprehensive list of geometric theorems here:
https://tutor.hix.ai

This is also the source from which I retrieved the theorem I posted in the above answer.

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Answer 2

To prove that two angles are supplementary, you need to show that their measures sum up to 180 degrees. This can be demonstrated through various methods depending on the context of the problem or the type of angles involved. Here are some common approaches:

  1. Direct Angle Measurement: Measure the two angles using a protractor or other measuring tool. If the sum of their measures equals 180 degrees, then they are supplementary.

  2. Algebraic Proof: If the angles are represented algebraically, set up an equation using the measures of the angles. Then solve the equation to show that their sum equals 180 degrees.

  3. Geometric Properties: Utilize geometric properties such as vertical angles, linear pairs, or corresponding angles to establish the relationship between the angles and prove their supplementary nature.

  4. Theorem or Postulate: Apply relevant theorems or postulates from geometry that directly state or imply that certain pairs of angles are supplementary. Use the given information and apply the theorem to prove the angles are supplementary.

Regardless of the method chosen, the key is to demonstrate that the sum of the measures of the two angles equals 180 degrees, thereby proving their supplementary relationship.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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