Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

Martin draws a square with the vertices A, B, C, D, and a regular hexagon with side O, C, where O is the center of the square. What is the measure of angle alpha?  Let's first consider the quadrilateral formed by the vertex alpha, O, C, and D. We know that the sum of the angles within a quadrilateral are 360 degrees.  Because A, B, C, D is a square, we know D is 90 degrees, and because O, C is part of a regular hexagon, we know angle O is 120 degrees.  We also know that angle C is equal to 45 degrees because O, C bisects the right angle. Therefore, we can just do some simple algebra and find that angle alpha must be 105 degrees.

Video Summary

Martin analyzes the angles in a geometric figure involving a square and a regular hexagon. Within a quadrilateral formed by vertices alpha, O, C, and D, he calculates the angles: D is 90 degrees (from the square), O is 120 degrees (from the hexagon), and C is 45 degrees (since O, C bisects a right angle). Using the angle sum property of quadrilaterals (360 degrees), he concludes that angle alpha measures 105 degrees.

Keywords

geometric analysis

square

regular hexagon

quadrilateral angles

angle calculation