Divide 91.53 to the lowest terms
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Nick cut a circular cookie into 5 equal slices. What is the angle measure of each slice?
A.
36°
B.
72°
C.
108°
D.
144°
B. 72°
A circle has 360 degrees. Nick cut the circle into 5 equal slices, so each slice will have an angle measure of:
360 degrees ÷ 5 = 72 degrees
Which is the measure of the angle shown on the protractor?
Obtuse angle on a protractor. One ray is pointing to 0 degrees and the other ray is pointing to 170 degrees or 10 degrees.
A.
10°
B.
20°
C.
160°
D.
170°
2 / 7
D. 170°
∠
A
B
C
measures 146°. Which is the measure of
∠
A
B
D
?
Angle DBC is a straight angle. Ray BA intersects angle DBC at point B.
A.
34°
B.
44°
C.
134°
D.
180°
B. 44°
If angle ABC measures 146°, then angle DBC (a straight angle with ABC) measures:
180° - 146° = 34°
Since angle ABD and angle DBC are adjacent angles that form a straight angle, the measure of angle ABD is:
180° - 34° = 146°
Finally, since angle ABD and angle ABC are alternate interior angles, they have the same measure. Therefore, the measure of angle ABD is also 146°.
We now need to find the measure of angle ABD minus the measure of angle ABC to find the measure of angle ABD:
146° - 102° = 44°
Therefore, the measure of angle ABD is 44°.
The hands of clock form a 120° angle. What time is it?
A.
2:00
B.
4:00
C.
6:00
D.
9:00
C. 6:00
The minute hand of a clock rotates 360 degrees in 60 minutes (1 hour), or 6 degrees per minute. The hour hand rotates 360 degrees in 12 hours, or 30 degrees per hour.
Let's call "x" the number of minutes that have passed since the last full hour. The position of the minute hand can be represented by:
6x
The position of the hour hand can be represented by:
30(t + x/60)
where "t" is the number of full hours that have passed.
We know that the angle between the hands of the clock is 120 degrees. This means that:
6x - 30(t + x/60) = 120
Simplifying this equation, we get:
360x - 180(t + x/60) = 720
Multiplying both sides by 60, we get:
21600x - 10800(t + x) = 43200
Simplifying, we get:
10800t = 21600x - 43200
Dividing both sides by 10800, we get:
t = 2x - 4
This means that the hour hand is two hours (or 60 degrees) behind the minute hand. Since the angle between the hands is 120 degrees, the minute hand must be pointing directly at the "6" on the clock, and the hour hand must be pointing halfway between the "4" and the "5". This means that it is 6 o'clock.
What is an obtuse angle?
A.
forms a straight line
B.
forms a square corner
C.
measures less than a right angle
D.
measures more than a right angle, but less than a straight angle