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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Taylor Swift is measuring the steepness of a ski slope to rate the slope's difficulty. Every 10 meters, Taylor Swift holds out a string with a weight at the bottom, and measures the angle between the string and the slope. Taylor Swift'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.
Taylor Swift is measuring the steepness of a ski slope to rate the slope's difficulty. Every 10 meters, Taylor Swift holds out a string with a weight at the bottom, and measures the angle between the string and the slope. Taylor Swift'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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Rihanna is a marine biologist attempting to track populations of sharks. Using the vessel’s instruments, Rihanna 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 Rihanna’s ship takes instructions in degrees right or left of straight ahead (e.g. $$30^\circ$$ right). What instructions would Rihanna have to give to the ship in order to pursue either population?
Rihanna is a marine biologist attempting to track populations of sharks. Using the vessel’s instruments, Rihanna 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 Rihanna’s ship takes instructions in degrees right or left of straight ahead (e.g. $$30^\circ$$ right). What instructions would Rihanna 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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The circumference of the earth is approximately 24,000 miles. Suppose Michael Vick is on a plane that passes through the (0,0) point and flies 4,000 miles South and 2,000 miles West. Give Michael Vick's position: _____$$^\circ S$$ _____$$^\circ W$$.
The circumference of the earth is approximately 24,000 miles. Suppose Michael Vick is on a plane that passes through the (0,0) point and flies 4,000 miles South and 2,000 miles West. Give Michael Vick's position: _____$$^\circ S$$ _____$$^\circ W$$.
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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 Wale 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 Wale’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 Wale 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 Wale’s position: _____$$^\circ N$$ _____$$^\circ W$$.
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