Add and Subtract Angle Measures
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4th Grade Math › Add and Subtract Angle Measures
A clock face shows that the hour hand and minute hand form different angles with the 12 o'clock position. The hour hand makes a $$90°$$ angle with 12 o'clock, and the minute hand makes a $$54°$$ angle with 12 o'clock. Both hands are on the same side of 12 o'clock. What is the angle between the two hands?
$$54°$$
$$36°$$
$$90°$$
$$144°$$
Explanation
Since both hands are on the same side of 12 o'clock, the angle between them is the difference between their individual angles from 12 o'clock: 90° - 54° = 36°. Choice A adds the angles (90° + 54°), while choices C and D repeat one of the given angles.
A surveyor measures a large angle at a construction site. The angle measures $$137°$$ and is composed of four smaller, non-overlapping angles. Three of these angles measure $$28°$$, $$35°$$, and $$41°$$. What is the measure of the fourth angle?
$$69°$$
$$241°$$
$$104°$$
$$33°$$
Explanation
The four angles must add to 137°: 28° + 35° + 41° + fourth angle = 137°. First, 28° + 35° + 41° = 104°. So the fourth angle = 137° - 104° = 33°. Choice B gives the sum of the three known angles (104°), choice C adds all given measurements (137° + 28° + 35° + 41°), and choice D gives an incorrect calculation.
Tommy draws an angle that measures $$156°$$. He then draws a ray inside this angle that creates two smaller angles. One of the smaller angles measures $$89°$$. If Tommy wants the other smaller angle to measure $$75°$$, by how many degrees is he off from his target?
$$2° ext{ too small}$$
$$2° ext{ too large}$$
$$8° ext{ too large}$$
$$8° ext{ too small}$$
Explanation
The actual measure of the second angle is 156° - 89° = 67°. Tommy wants it to be 75°, so he needs 75° - 67° = 8° more. His current angle is 8° too small. Choice B reverses the direction, while choices C and D use an incorrect difference of 2°.