Math is not my strongest subject : /

The angles with measures (5x + 4y)º and 74º are congruent because they form a pair of alternate interior angles between the parallel horizontal bars, so

5x + 4y = 74

The other two labeled angles are also congruent because they are corresponding interior angles that occur between the parallel vertical bars, so

20x + 4y = 164

Then

(20x + 4y) - (5x + 4y) = 164 - 74

(20x - 5x) + (4y - 4y) = 90

15x = 90

x = 6

which means

5*6 + 4y = 74

4y = 44

y = 11

perimeter = 10 +  √10  units

explanation:

first, we will need to get the length of each line using the distance formula which is as follows:

distance = 

1- length of ab:

ab =   = 5 units

2- length of ac

length of ac is the same as ab = 5 units

3- length of bc:

bc =   =  √10  units

now, we can get the perimeter by adding the side lengths as follows:

perimeter = 5 + 5 +  √10

perimeter = 10 +  √10  units

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