4.MD.7: Recognize angle measure as additive. When an angle is...

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.



Use the illustration below to determine the measure of \(\angle APC\).

Use the illustration below to determine the measure of \(\angle APC\).
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Adrian Peterson is measuring the steepness of a ski slope to rate the slope's difficulty. Every 10 meters, Adrian Peterson holds out a string with a weight at the bottom, and measures the angle between the string and the slope. Adrian Peterson's survey yields the following measurements: \(30^\circ\), \(40^\circ\), \(51^\circ\), \(78^\circ\), \(90^\circ\). Use your protractor to construct a drawing of the slope.
Adrian Peterson is measuring the steepness of a ski slope to rate the slope's difficulty. Every 10 meters, Adrian Peterson holds out a string with a weight at the bottom, and measures the angle between the string and the slope. Adrian Peterson's survey yields the following measurements: \(30^\circ\), \(40^\circ\), \(51^\circ\), \(78^\circ\), \(90^\circ\). Use your protractor to construct a drawing of the slope.
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Nicki Minaj is a marine biologist attempting to track populations of sharks. Using the vessel’s instruments, Nicki Minaj detects one population at \(50^\circ\) and another population at \(110^\circ\).
(a) What is the measure of the angle between the two populations?
(b) Suppose that Nicki Minaj’s ship takes instructions in degrees right or left of straight ahead (e.g. \(30^\circ\) right). What instructions would Nicki Minaj have to give to the ship in order to pursue either population?
Nicki Minaj is a marine biologist attempting to track populations of sharks. Using the vessel’s instruments, Nicki Minaj detects one population at \(50^\circ\) and another population at \(110^\circ\).
(a) What is the measure of the angle between the two populations?
(b) Suppose that Nicki Minaj’s ship takes instructions in degrees right or left of straight ahead (e.g. \(30^\circ\) right). What instructions would Nicki Minaj have to give to the ship in order to pursue either population?
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Lil Wayne is a video game designer developing a game with a three-dimensional first-person perspective. Lil Wayne needs to translate the motion of the joystick into right-left rotations and up-down head movements. Lil Wayne logically chooses a reference line that is straight ahead, and measures rotations in degrees up, down, right and left. The player’s perspective rotates \(90^\circ\) for every one second that the player holds the joystick in that direction. Suppose that the player starts looking straight ahead and performs the following movements: 1 second right, \(1/2\) seconds up, \(2/3\) seconds left, \(1/6\) seconds down. What is the player’s new perspective in degrees?
Lil Wayne is a video game designer developing a game with a three-dimensional first-person perspective. Lil Wayne needs to translate the motion of the joystick into right-left rotations and up-down head movements. Lil Wayne logically chooses a reference line that is straight ahead, and measures rotations in degrees up, down, right and left. The player’s perspective rotates \(90^\circ\) for every one second that the player holds the joystick in that direction. Suppose that the player starts looking straight ahead and performs the following movements: 1 second right, \(1/2\) seconds up, \(2/3\) seconds left, \(1/6\) seconds down. What is the player’s new perspective in degrees?
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Position on the earth’s surface is measured in degrees N/S and degrees E/W. The 0,0 point occurs in the Gulf of Guinea, south of Ghana. Suppose that Selena Gomez boards a ship that passes through the (0,0) point and travels West for a quarter of the Earth’s circumference, and North for an eighth of the Earth’s circumference. Give Selena Gomez’s position: _____\(^\circ N\) _____\(^\circ W\).
Position on the earth’s surface is measured in degrees N/S and degrees E/W. The 0,0 point occurs in the Gulf of Guinea, south of Ghana. Suppose that Selena Gomez boards a ship that passes through the (0,0) point and travels West for a quarter of the Earth’s circumference, and North for an eighth of the Earth’s circumference. Give Selena Gomez’s position: _____\(^\circ N\) _____\(^\circ W\).
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The circumference of the earth is approximately 24,000 miles. Suppose Azealia Banks is on a plane that passes through the (0,0) point and flies 4,000 miles South and 2,000 miles West. Give Azealia Banks's position: _____\(^\circ S\) _____\(^\circ W\).
The circumference of the earth is approximately 24,000 miles. Suppose Azealia Banks is on a plane that passes through the (0,0) point and flies 4,000 miles South and 2,000 miles West. Give Azealia Banks's position: _____\(^\circ S\) _____\(^\circ W\).
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Add and subtract angles



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