Grades 9-10 Video Solutions 2021-video 2021 9-10/19

Video Transcription

Problem number 19 states, what is the sum of the measure of the six marked angles in the picture?  So in our picture here, we have a rectangle that is split up into two sections by this line. Let's consider this top section.  If we count the sides of this polygon, we can see that it has 10 sides. We know that the sum of the angles of a polygon can be calculated by a formula that states  that 180 times the number of sides of the polygon minus 2 is equal to the sum of the angles of the polygon. This polygon has 10 sides, so we would do 10 minus 2 times 180.  10 minus 2 is 8, 8 times 180 is 1,440 degrees. This however is not the answer, because this is the sum of all the angles in the polygon, but we only want to add up the shaded ones.  Luckily, all the ones that we do not want to add, we know the values of, because we know that they are the corners of the rectangle.  We know that we have four corners that are 90 degrees each. This means that in total, the discarded angles total to 360 degrees.  So let's subtract this sum from the shaded polygon's angle sum. And 1,440 minus 360 gets us 1,080 degrees.  So the question asked us, what is the sum of the measure of the six marked angles in this picture? The answer is 1,080 degrees. Letter C.

Video Summary

The problem involves calculating the sum of six marked angles within a polygon formed by a rectangle divided into two sections. The polygon has 10 sides, so using the formula for the sum of interior angles, \(180 \times (10 - 2)\), the total is 1,440 degrees. Since 360 degrees (the four 90-degree corners of the rectangle) are not part of the marked angles, this is subtracted from 1,440, resulting in 1,080 degrees. Therefore, the sum of the six marked angles is 1,080 degrees, corresponding to answer choice C.

Keywords

polygon

interior angles

rectangle

geometry

sum of angles