Explanations and Solutions to California Standards Released Geometry Test Questions

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SOLUTIONS TO RELEASED GEOMETRY TEST QUESTIONS

The following contains complete solutions to the released test questions for the California Geometry Standards Test. The original questions are here




Solutions to California Released Geometry Test

Questions 55 Through

Problem 55  Solution
Sum of Angles of Pentagon (n-2)180 =5*180 = 540

20x = 540 + 20
20 x = 560
x = 28

6*28 + 2
168 + 2 = 170

Problem 56 Solution

65 (12-2)*180 =1800

1800/12 = 900/6 = 300/2 =150 Degree Interior Angle

Exterior Angle = 180 - 150 = 30

Sum of Exterior Angles = 12*30 = 360


Answer B: Exterior Angle = 30 Degrees

Problem 57 Solution

The triangle that contains angle 1 has two angles

equal to  54(90-36) and 92 (180-88). Since the sum

of the angles in a triangle are equal to 180, the

measure of m1 is 180 - 54 - 92 = 34 degrees

Answer A: 34 Degrees


Problem 58 Solution

The measure of angle V is 48 degrees (supplementary angles).

The sum of angle V and Y is 52 + 48 = 100 Degrees

The measure of angle WZX = angle VZY = 180 - 100 = 80

Answer: A 80 Degrees


Problem 59 Solution

Find the measure of  the exterior angle of a regular hexagon (6 sides)

Sum of Angles = (n-2)180 = (6-2)*180 = 720

Interior Angle = 720 / 6 = 360/3 = 120

Exterior Angle = 180 -120 = 60

Answer: B  60 Degrees

Problem 60 Solution

The area of the inner square is "not" equal  to half the area of the outer square.

Pythagorean Formula Proof

The area of the outer square is equal to the area of the  inner square plus the area of the 4 inner triangles.

Area of inner square is c*c
Area of one inner right triangle = (1/2)bh = (1/2)ab

Area of 4 inner right triangles = 2ab

Area of outer square = (a+b)(a+b)

Area of outer square = Area of inner square + 4(area inner right triangle)

(a+b)(a+b) =  c*c + 2ab
a*a + 2ab + bb = c*c +2ab

a*a + b*b = c*c  Pythagorean's Formula

Answer: C

Problem 61 Solution

Given right triangle’s hypotenuse of  5. Leg, 2, find other length of other leg

4 + b*b = 25
b*b = 21
b = sqrt (21)

Answer: B,  The square root of 21

Problem 62 Solution

60*60 + 32*32 = c*c
4624 = c*c
c = Square Root (4624)
c = 68

60 +  32  - 68 = 24

Answer: A 24 miles


Problem 63 Solution

8*8 - 7*7 = 64 - 49 = 15

x = Square Root (15)

Answer: C, Square Root of 15


Problem 64 Solution

A line through P parallel to line l best describes the construction. The four arc marks indicate that a parallel line is under construction. The arcs define two points that are the same perpendicular distance from the line that passes through P.  The key to the problem is "best." Line l is somewhat ambiguous.


Problem 65 Solution

The first step in the construction of a line that bisects an angle is to draw an arc through the two rays of the angle centered at the vertex of the angle. The next step is to construct two arcs from the points of intersection of the first arc with the rays of the angles.

Answer: D


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