Answer:
53.3 degrees
Step-by-step explanation:
∆DEF and ∆RSQ are similar. We know this, because the ratio of their corresponding sides are equal. That is:
DE corresponds to RS
EF corresponds to SQ
DF corresponds to RQ.
Also <D corresponds to <R, <E corresponds to <S, and <F corresponds to <Q.
The ratio of their corresponding sides = DE/RS = 6/3 = 2
EG/SQ = 8/4 = 2
DF/RQ = 4/2 = 2.
Since the ratio of their corresponding sides are equal, it means ∆DEF and ∆RSQ are similar.
Therefore, their corresponding angles would be equal.
Thus, m<Q = m<F
Let's find angle F
m<F = 180 - (98 + 28.7)
m<F = 53.3°
Since <F corresponds to <Q, therefore,
m<Q = 53.3°
The answers are C and B.
Answer A has infinite solutions, and D has no solutions
1) It's best to draw out a picture of a rectangle and label each corner with the coordinates given: Let's say (-5, 2) is point A, (-5, -2 1/3) is point B, (2 1/2, 2) is point C, and (2 1/2, -2 1/3) is point D.
2) That being said, line AB is one side of the rectangle, BC is another, CD is another, and lastly, AD is the fourth side.
3) We can use the distance formula and plug in the coordinates of each line to find how long every side is. Then you just need to solve it.
For example: if I want to find how long side AB is, I would use the point A (-5, 2) and B (2 1/2, 2) and plug them into the distance formula, where (-5, 2) is (x1, x2) and (2 1/2, 2) is (x2, y2) and solve that.
4) Repeat this process with side BC, CD, and AD, and add the results together. This will be your final answer; the perimeter of the rectangle.
X equals 60 degrees (80-20=60)
