Please help I've had to repost this three times...

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  A: 1; B: 3; C: 2; D: 2; E: 4

Step-by-step explanation:

The sum of angles in a triangle is 180°. This statement is called the "Triangle Sum Theorem."

Statement line 2 is a list of the three angles in the triangle. The one missing is angle S (tile 1, answer A). The missing theorem description is tile 3, answer B.

Statement lines 3 and 4 are algebra. Line 3 is a substitution of a number for the measure of angle Q. Since angle Q is marked as a right angle, its measure is 90° (tile 2, answer C). Line 4 subtracts that 90° from both sides of the equation, resulting in a statement that the sum of the two angles is 90° (tile 2, answer D).

Finally, we declare the angles complementary because we've shown their sum is 90°. That's a matter of definition. (tile 4, answer E).

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