In the given diagram, ∠4 = 45°, ∠5 = 135°, and ∠10 = ∠11. part a: solve for the values of the remaining angles. show all your work for full credit. part b: use complete sentences to describe the angle relationship between the following angle pairs: 1. ∠4 and ∠1 2. ∠7 and ∠5 3. ∠9 and ∠10

A) ∠9 = ∠10 = ∠11 = ∠12  = 90°

∠2 = ∠3 = ∠5 = ∠8 = 135°

∠1 = ∠4 = ∠6 = ∠7 = 45°

B) 1. ∠4 and ∠1 -> vertical angles

2. ∠7 and ∠5 -> supplementary

3. ∠9 and ∠10 -> supplementary

Step-by-step explanation:

Data

∠4 = 45°∠5 = 135°∠10 = ∠11

The following are vertical angles, so they are congruent:

∠1 ≅ ∠4

∠3 ≅ ∠2

∠11 ≅ ∠9

∠10 ≅ ∠12

∠7 ≅ ∠6

∠5 ≅ ∠8

From here and data, it is deduced that

∠11 ≅ ∠9 ≅ ∠10 ≅ ∠12

From the picture, the addition of them is equal to 360°, then:

∠11 + ∠9 + ∠10 + ∠12 = 360°

4*∠11 = 360°

∠11 = 360°/4

∠11 = 90° = ∠10 = ∠9 = ∠12

∠2 and ∠4 are supplementary, then:

∠2 + ∠4 = 180°

∠2 = 180° - 45°

∠2 = 135°

∠7 and ∠5 are supplementary, then:

∠7 + ∠5 = 180°

∠7 = 180° - 135°

∠7 = 45°

A. 1=45 degress because 4 and 1 are vertical angles which means they are equal.

2= 135 degrees because angle 4+2 equals 180 degrees(straight line) so since we know that angle 4 is 45 degrees, you can subtract it from 180, which is 135.

3=135 degrees because it is vertical angles with angle 2 which is 135 degrees.

6= 45 degrees because we know angle 5 is 135 degress. So, 135+angle 6=180(straight line). So if you subtract 135 from 180, you get 45.

7=45 degrees because it is vertical angles with angle six which is 45 degrees.

8= 135 degrees because it is vertical angles with angle five which is 135 degrees.

10= 90 degrees, because we know that angle 10 and 11 are equal and that they equal 180 degrees together(straight line). So, if you divide 180 by two(two angles) you will get 90 degrees.

11= 90 degrees for the same reason as angle 10.

9=90 degrees because it is vertical angles with angle 11 which is 90 degrees.

12=90 degrees because it is vertical angles with angle 10 which is 90 degrees.

B.

1) 4 and 1 are vertical angles which makes them equal

2) 7 and 5 are supplementary angles, which means they add up to 180 degrees.

3) 9 and 10 are also supplementary angles, but the line dividing them is their angle bisector, splitting them into two equal parts, 90 degrees and 90 degrees.

Sorry this explaination is so long. I hope it's helpful!!

Hi.. did you ever get the answer to this question? What answer did you put? I need it please

Step-by-step explanation:

Solution with full workings

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Step-by-step explanation:

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It’s obvio that’s 1)4 2)6 3)10

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part a.

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part b.1. vertical angles

2. linear pair

3. linear pair