Question

The sum of the interior angles of each polygon is 360°. In the diagram, DEFG=SPQR.Find the values of x and y

R
D
4 ft E
106°
(y + 38)
84°
(3y + 12°
S
x ft
6 ft
F
Р

Answer 1

Since the polygons DEFG and SPQR are congruent

That means

DE = SP

EF = PQ

FG = QR

DG = SR

AND

mmmm

Since DE = x and SP = 3, then

x = 3

Since < S = 107 degrees and

In the polygon DEFG, the sum of the angles is 360 degrees, then

107 + (y + 3) + 83 + (y + 1) = 360

Add the like terms on the left side

(107 + 3 + 83 + 1) + (y + y) = 360

194 + 2y = 360

Subtract 194 from both sides

194 - 194 + 2y = 360 - 194

2y = 166

Divide both sides by 2

y = 83

The value of x is 3 and the value of y is 83