If $xy=15$ and  $x+y=11,$ what is  $x^2+y^2?$  

(a)  

What is the supplement of the complement of the angle which measures 67^o?

(a)  

If the diagonals of rectangle ABCD meet at E and $\angle AEB=30\degree,$ what is  $\angle EBC?$   

(a)  

Two vertices of an equilateral triangle are at the origin and at $\left(2\sqrt{3},0\right).$ How long is the height of the triangle? 

(a)  

Let ABC be an isosceles right triangle with AC as its hypotenuse, and let D and E be midpoints on AB and AC, respectively, such that  $DE\parallel BC.$  If AB = BC = 5 and DE = 3, what is the area of the trapezoid DECB?

(a)  

Triangle ABC is isosceles with AB = AC. Let D be the foot of the altitude from A on BC, and let E be the point on the side AC such that DE bisects $\angle ADC.$ If  $\angle DEC=53\degree,$ what is  $\angle BAC?$ 

(a)  

Let ABCD be a square. Three parallel lines $ℓ_1,\ ℓ_2,$ and  $ℓ_3$ pass through A, B and C, respectively. The distance between $ℓ_1$ and  $ℓ_2$ is 5, and the distance between $ℓ_2$ and $ℓ_3$ is 7. Find the area of the square. 

(a)