Answer ASAP In the given diagram, ∠4 = 45°, ∠5 = 135° and ∠10 = ∠11 Part A: Solve for the values of the remaining angles. Show all of your work. 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

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°

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

21

step-by-step explanation: