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QUESTION NO: 1
In the diagram above, what is the area of the rectangle?
A. 6ab square units
B. 8ab square units
C. 9b2 square units
D. 12ab square units
E. 16b square units
Answer: B
Explanation/Reference:
The y-axis divides the rectangle in half. Half of the width of the rectangle is a units to the left of the y- axis
and the other half is a units to the right of the y-axis. Therefore, the width of the rectangle is 2a units.
The
length of the rectangle stretches from 3b units above the x-axis to b units below the x-axis.
Therefore, the
length of the rectangle is 4b units. The area of a rectangle is equal to lw, where l is the length of the rectangle and w is the width of the rectangle. The area of this rectangle is equal to (2a) (4b) = 8ab square
units.
QUESTION NO: 2
In the diagram above, lines K and L are parallel, and lines Mand N are parallel. If b = 8, then a =?
Answer: 11
Explanation/Reference:
The labeled angle formed by lines M and K and the supplement of the labeled angle formed by lines L and
N are alternating angles. Therefore, they are congruent. The angle labeled (10a + 5) and its supplement,
which is equal to (8b + 1), total 180 degrees: (10a + 5) + (8b + 1) = 180. If b = 8, then:
(10a + 5) + (8(8) + 1) = 18010a + 70 = 18010a = 110a = 11
QUESTION NO: 3
Point A of rectangle ABCD is located at (-3, 12) and point C is located at (9,5).What is the area of rectangle ABCD?
Answer: 84
Explanation/Reference:
If point A is located at (-3,12) and point C is located at (9,5), that means that either point B or point D has
the coordinates (-3,5) and the other has the coordinates (9,12). The difference between the different x
values is 9 - (-3) = 12 and the difference between the different y values is 12 - 5 = 7. The length of the rectangle is 12 units and the width of the rectangle is seven units. The area of a rectangle is equal to its
length multiplied by its width, so the area of ABCD= (12)(7) = 84 square units.
QUESTION NO: 4
In the diagram above, if angle OBE measures 110 degrees, what is the measure of arc AC?
A. 20 degrees
B. 40 degrees
C. 55 degrees
D. 80 degrees
E. cannot be determined
Answer: B
Explanation/Reference:
Angles OBE and DBO form a line. Since there are 180 degrees in a line, the measure of angleDBOis180
1 10= 70 degrees. OB and DO are radii, which makes triangle DBO isosceles, and angles ODB and DBO congruent. Since DBO is 70 degrees, ODB is also 70 degrees, and DOB is 180 (70 + 70) =180 140 = 40 degrees. Angles DOB and AOC are vertical angles, so the measure of angle AOC is also 40 degrees.
Angle AOC is a central angle, so its intercepted arc, AC, also measures 40 degrees.
QUESTION NO: 5
In the diagram above, side OB side OC. Which of the following is the measure of minor arc BC?
A. 27.5 degrees
B. 45 degrees
C. 55 degrees
D. 70 degrees
E. 110 degrees
Answer: D
Explanation/Reference:
LineOB lineOC, which means the angles opposite lineOBandOC(anglesCandB) are congruent. Since
angleB= 55 degrees, then angleC= 55 degrees. There are 180 degrees in a triangle, so the measure of angle O is equal to 180 (55 + 55) = 180 110 = 70 degrees. Angle O is a central angle. The measure of its intercepted arc, minor arcBC, is equal to the measure of angle O, 70 degrees.
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Updated: May 26, 2022