Solve for x in the diagram below “x + 54”
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Answer:
Step-by-step explanation:
1). WXYZ is a rectangle,
Properties of a rectangle,
i). Opposite sides are equal and parallel.
ii). All interior angles measure 90°.
iii). Diagonals are equal in measure.
a). WY = ZX = 30
Therefore, ZT =
b). WY = ZX = 45
c). Since, WY = ZX,
(4b - 16) = (3b + 5)
4b - 3b = 16 + 5
b = 21
2). GOAT is a rhombus and m∠OGA = 35°,
a). m∠TGA = m∠OGA = 35°
b). m∠GXO = 90°
c). m∠GXT = 90°
d). Since adjacent angles of a rhombus are supplementary,
m∠OGT + m∠GTA = 180°
70° + m∠GTA = 180°
m∠GTA = 110°
m∠GTO =
=
= 55°
e). Since, opposite angles of a rhombus are equal,
m∠OGT = m∠OAT = 70°
f). m∠GOA = m∠GTA = 110°