Answer:
Step-by-step explanation:
19). Angles measuring 90° and (21x + 6)° are Alternate exterior angles.
Therefore, 21x + 6 = 90
2x = 90 - 6
2x = 84
x = 42
21). Angles measuring 60° and (8x - 4)° are Alternate interior angles,
8x - 4 = 60
8x = 60 + 4
x = 
x = 8
23). Since, angles measuring (-1 + 14x)° and (12x + 17)° are Alternate exterior angles
Therefore, (-1 + 14x) = (12x + 17)
14x - 12x = 17 + 1
2x = 18
x = 9
25). Both the angles (x + 96)° and (x + 96)° are consecutive interior angles.
Therefore, (x + 96)° + (x + 96)° = 180° [Property of consecutive interior angles]
2x + 192 = 180
2x = 180 - 192
2x = -12
x = -6
Now measure of (x + 96)° = -6 + 96
= 90°
26). Both the angles (20x + 5)° and (24x - 1)° are consecutive interior angles.
Therefore, (20x + 5)° + (24x - 1)° = 180°
44x + 4 = 180
44x = 176
x = 4
The number of possible combinations is given by
... C(18, 3) = 18!/(3!(18-3)!) = 18·17·16/(3·2·1) = 816 . . . . possible combinations
_____
There are 18 ways to choose the first one; 17 ways to choose the second one, and 16 ways to choose the 3rd one. The same 3 students can be chosen in any of 3! = 6 different orders, so the product 18·17·16 must be divided by 6 to get the number of possible combinations in which order doesn't matter.
The postulate of the corresponding angles establishes that when a transversal line cuts two parallel lines, the corresponding angles are congruent. These angles are on the same side of the parallel lines and on the same side of the transversal line.
Then, if we based on this definition and analize the figure attached, we can notice that the angles ∠1 and ∠3 are corresponding angles, so they are congruent. In this case the angle ∠1 is internal and the angle ∠3 is external.
The answer is: ∠1 and ∠3 are congruent (See the image attached).
