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
