Question

Please help solve 1, and 2

Answer 1

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 =
`(1)/(2)(ZX)`

`ZT=15`

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 =
`(1)/(2)(m\angle GTA)`

=
`(1)/(2)(110^(\circ))`

= 55°

e). Since, opposite angles of a rhombus are equal,

m∠OGT = m∠OAT = 70°

f). m∠GOA = m∠GTA = 110°