Question Video: Finding the Smallest Positive Angle Equivalent to a Given One | Nagwa Question Video: Finding the Smallest Positive Angle Equivalent to a Given One | Nagwa

# Question Video: Finding the Smallest Positive Angle Equivalent to a Given One Mathematics • First Year of Secondary School

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Find the smallest positive equivalent of 788°.

02:03

### Video Transcript

Find the smallest positive equivalent of 788 degrees.

Let’s see if we can visualise this. If we began at zero degrees and we make a full turn, we’ve gone 360 degrees. We’re interested though in 788 degrees. If we continue where we left off and make a second complete turn, we’ve gone 720 degrees. To make it from 720 to 788, we’ll need to go a bit further. 788 minus 720 is 68. After we’ve done our second turn, we need to go 68 degrees further. At this point, we’ve gone around twice and then an additional 68 degrees, for a total of 788 degrees. And so we can say 68 degrees is the equivalent to 788 degrees.

This first method of solving requires sketching an image, but we can solve this problem without doing that. We know we need to go 788 degrees. And we know that 360 degrees is one full turn. If we divide 788 by 360, we’ll find out how many full turns 788 degrees is. When we do that, we get 2.18 repeating. The whole number two tells us that we have two full turns and 0.18 repeating, partial turn. To convert this decimal back in two degrees, we multiply it by 360 degrees, which gives us 68 degrees. The smallest positive equivalent of 788 degrees is 68 degrees.

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