Question Video: Finding a Related Angle Using a Given Diagram Mathematics

State the smallest positive angle that is equivalent to the angle shown.

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Video Transcript

State the smallest positive angle that is equivalent to the angle shown.

Remember, when we think about angles in standard position, the angle is measured by the amount of rotation from the initial side to the terminal side. An angle that is measured in a counterclockwise direction is said to be positive, whilst if it’s measured in a clockwise direction, we say that it’s negative. We also say that if two angles in standard position have the same terminal side, they’re called coterminal angles. So let’s examine the diagram.

We have an angle that is measured in a clockwise direction 340 degrees. So it’s negative 340. And we’re looking to find the measure of the coterminal angle to this, the one that lies in the first quadrant. We can therefore use a simple angle fact, and that is the fact that angles around a point sum to 360 degrees. The angle measured in a clockwise direction is simply 340 degrees. It’s the absolute value of negative 340. So if we define the angle that we’re trying to calculate to be equal to 𝜃, then we can say that 𝜃 plus 340 equals 360.

To solve for 𝜃, we’ll simply subtract 340 from both sides. 360 minus 340 is 20. And so the smallest positive angle that’s equivalent to negative 340 degrees is 20 degrees.

We might also observe that the question asked us to find the smallest positive angle. That’s because we can find an infinite number of angles by simply completing another full turn in a counterclockwise direction, so there will be a number of positive angles equivalent to this that can be found by adding multiples of 360 degrees to 20.

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