The value of z and t obtained using the properties of an isosceles trapezoid are;
z = 1.4, and t = 12.6
The steps used to find the possible values of z and t are as follows;
The diagram of the isosceles trapezoid is left out; The order of the letters in the name of the trapezoid, KDSX, indicates that the angles K and X are non adjacent sides of the isosceles trapezoid Whereby the base angles of the isosceles trapezoid are ∠K and ∠X, we get;
∠K ≅ ∠X (Base angles of an isosceles trapezoid)
m∠K = m∠X
35·z - 20 = 15·z + 8
35·z - 15·z = 8 + 20
20·z = 28
z = 28/20
z = 1.4
Therefore; m∠K = 35 × 1.4 - 20
m∠K = 29°
m∠X = 29°
m∠S = (360 - 2 × 29)/2
m∠S = 151°
10·t + 25 = 151
10·t = 151 - 25
t = (151 - 25)/10
t = 12.6
The possible complete question obtained from a similar question found through search can be presented as follows;
KDSX is an isosceles trapezoid, as shown, where m∠K = (35·z - 20)°, m∠X = (15·z + 8)°, m∠S = (10·t + 25)°
The diagram of the isosceles trapezoid is left out; Please find attached the possible drawing of the isosceles trapezoid KDSX created with MS Word