Question

How do i solve this?

Answer 1

Answer:

x = 4

y = 9

Step-by-step explanation:

It is given that figure (NPQR) is a square. One property of a square is that all sides of a square are congruent. This property also applies to the given square, thus one can make the following statement;

PQ = NR

Substitute,

10y - 29 = 5y + 16

Inverse operations,

10y - 29 = 5y + 16

-5y           -5y

5y - 29 = 16

    +29   +29

5y = 45

/5     /5

y = 9

Another property of a square is that all of the interior angles of a square have a measure of (90) degrees. Moreover, the diagonals (segment connect non-adjacent vertices) bisect these angles. Thus, twice the measure of an angle formed between a side and a diagonal forms a (90) degree angle. Therefore, one can draw the following conclusion;

2(m<QPR) = 90

Substitute,

2(6x + 21) = 90

Simplify,

12x + 42 = 90

Inverse operations,

12x + 42 = 90

        -42  -42

12x = 48

/12     /12

x = 4