Grades 7-8 Video Solutions 2023-2023_7-8

Video Transcription

Question 19. Angelo drew two lines meeting at a right angle. What is the smallest number of extra  lines he could draw inside his right angle, as shown, so that for any of the values 10, 20, 30,  40, 50, 60, 70, and 80 degrees, a pair of lines can be chosen within the angle between them  equal to that value? Let's first start off by drawing out a right angle, which we know is 90  degrees. Then, our first line we will draw like so. It will divide us into 10 and 80 degrees.  Next, let's make the second smallest and get a 70 and 20 degree break. This also makes the  point in the middle 60 degrees. With this, we just need to draw one more line down the center.  This will give us 30 degrees on both sides, which will fulfill a 30 plus 20 or a 50 degree angle,  and a 30 plus 10 degree or 40 degree angle. This way, we have 10, 20, 30, 40, 50, 60, 70, and 80 degrees, all drawn out using only three lines. So our answer will be B, three.

Video Summary

To solve the problem of dividing a right angle such that chosen pairs of lines can form angles of 10, 20, 30, 40, 50, 60, 70, and 80 degrees, Angelo needs to draw three additional lines. The initial right angle is divided first into 10 and 80 degrees, then further with a second line to add divisions of 70, 20, and 60 degrees. The final line, placed strategically down the center, creates angles that sum up to the remaining necessary values. Thus, the smallest number of additional lines needed is three.

Keywords

right angle

divide angles

additional lines

angle divisions

geometry problem