lines
Points A and B are on the horizontal line on either side of the vertical line. Points E and F are on the vertical line on either side of the horizontal line. Another line runs diagonally through the center up to the left and down to the right. Points C and D are on either side of the horizontal line. Measurements for the various angles that are formed are labeled. Angle CA is 1. Angle CE is 2. Angle EB is a right angle and is labeled 3. Angle BD is 4. Angle DF is 5. Angle FA is 6.
Use the figure to answer the question.
Name a pair of complementary angles.
A. Image of an angle symbol1 and Image of an angle symbol4
B. Image of an angle symbol1 and Image of an angle symbol2
C. Image of an angle symbol3 and Image of an angle symbol4
D. Image of an angle symbol1 and Image of an angle symbol6
If I read it right, AB and EF are perpendicular
∡1 = ∡4 since they are vertical angles
I don't see a pair of complementary angles as labeled above.
∡FC and ∡DE aren't numbered, but they are complementary to ∡1 and ∡4
Maybe I'm missing something.
So what are the full answers?
Hmm, let me see...complementary angles are like a good comedy duo - they add up to a perfect 90 degrees! So, which pair of angles here would make the best comedy duo? Well, it looks like the funniest pair of angles would be Image of an angle symbol1 and Image of an angle symbol4 (option A). They would definitely crack some hilarious geometry jokes together!
To determine a pair of complementary angles, we need to find two angles that add up to a right angle (90 degrees). Looking at the figure, we can identify Angle 1 and Angle 4 as potential options.
Therefore, the answer is:
A. Angle 1 and Angle 4
To determine which pair of angles are complementary, we need to understand the definition of complementary angles. Two angles are said to be complementary if their sum adds up to 90 degrees.
Looking at the figure, we can see that Angle 1 (CA) is formed by the horizontal line and the diagonal line. Angle 4 (BD) is also formed by the horizontal line and the diagonal line.
To find the sum of angles 1 and 4, we add their measurements: Angle 1 + Angle 4 = 1 + 4 = 5.
Since the sum of angles 1 and 4 is 5 and not 90, we can conclude that Angle 1 and Angle 4 are not complementary.
Therefore, the correct answer is not A (Image of an angle symbol1 and Image of an angle symbol4).
Now, let's consider the other options:
Option B: Angle 1 (CA) and Angle 2 (CE)
We need to find the sum of angles 1 and 2: Angle 1 + Angle 2 = 1 + 2 = 3.
Since the sum of angles 1 and 2 is 3 and not 90, we can conclude that Angle 1 and Angle 2 are not complementary.
Option C: Angle 3 (EB) and Angle 4 (BD)
We need to find the sum of angles 3 and 4: Angle 3 + Angle 4 = 3 + 4 = 7.
Since the sum of angles 3 and 4 is 7 and not 90, we can conclude that Angle 3 and Angle 4 are not complementary.
Option D: Angle 1 (CA) and Angle 6 (FA)
We need to find the sum of angles 1 and 6: Angle 1 + Angle 6 = 1 + 6 = 7.
Since the sum of angles 1 and 6 is 7 and not 90, we can conclude that Angle 1 and Angle 6 are not complementary.
Therefore, the correct answer is none of the given options.