using the diagram where there is <CBD< DAC<ABC<EBA<ACB and D and C equal 45 degrees and B equals 90 degrees what is the measurement for <DAC and < ABC and <EBA and <ACB
In order to determine the measurements of the angles <DAC, <ABC, <EBA, and <ACB, we need to analyze the given diagram. The diagram states that angle D and angle C are equal to 45 degrees, and angle B is equal to 90 degrees.
Let's go step by step:
1. From the given information, we know that angle B is 90 degrees.
2. Based on the diagram, we can see that angle ABC is formed by angle B and angle DAC. Since angle B is a right angle (90 degrees), angle ABC is the sum of angle DAC and 90 degrees. Therefore, angle ABC = angle DAC + 90 degrees.
3. We're also given that angle D and angle C are equal to 45 degrees. So, angle DAC = angle D + angle C = 45 degrees + 45 degrees = 90 degrees.
4. Using the equation from step 2, we can substitute the value we found for angle DAC (which is 90 degrees) into angle ABC = angle DAC + 90 degrees. So, angle ABC = 90 degrees + 90 degrees = 180 degrees.
5. Now, let's look at angle EBA. From the diagram, we can see that angle EBA is formed by angle ABC and angle ACB. Since we found that angle ABC is 180 degrees, angle EBA is the sum of angle ACB and 180 degrees. Therefore, angle EBA = angle ACB + 180 degrees.
6. We can find angle ACB by subtracting angle DAC (90 degrees) from 180 degrees, as angle ACB = 180 degrees - angle DAC. So, angle ACB = 180 degrees - 90 degrees = 90 degrees.
7. Using the equation from step 5, we can substitute the value we found for angle ACB (which is 90 degrees) into angle EBA = angle ACB + 180 degrees. So, angle EBA = 90 degrees + 180 degrees = 270 degrees.
To summarize, based on the given diagram, we have found the measurements for the angles as follows:
- <DAC = 90 degrees
- <ABC = 180 degrees
- <EBA = 270 degrees
- <ACB = 90 degrees