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A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD, and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and ∠AEB and ∠CDB have the same measure. What is the value of x ?

In the figure above, lines l and m are parallel and lines s and t are parallel. If the measure of ∠1 is 35°, what is the measure of ∠2 ?

• 35°

• 55°

• 70°

• 145°

In the figure above, lines k, l , and m intersect at a point. If x+y=u+w, which of the following must be true?

I. x=z

II. y = w

III. z=t

• I and II only

• I and III only

• II and III only

• I, II and III

Two isosceles triangles are shown above. If 180 − z = 2y and y = 75, what is the value of x?

Circle A has a radius of 3n and circle B has a radius of 129n, where n is a positive constant. The area of circle B is how many times the area of circle A?

• 43

• 86

• 129

• 1849

In the figure shown, line c intersects parallel lines s and t. What is the value of x ?

• 4

• 8

• 16

• 32

The circle shown has center O, circumference 144π, and diameters PR and QS. The length of arc PS is twice the length of arc PQ. What is the length of arc QR ?

• 24π

• 48π

• 72π

• 96π