Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem11

Video Transcription

Question number 11. Triangle RZT, the one on the right here, is the image of the equilateral triangle KZM on the left upon rotation  by 130 degrees clockwise around the point Z. What is the measure of the angle RKM?  So in the larger diagram below,  the angle RKM is the angle indicated here. That's the angle we are looking for.  Now, we know that the two shaded triangles are isosceles  and in fact equilateral. So we can make an observation that the triangle KZR is in fact isosceles and this fact will help us compute the two angles marked here.  We know that that angle is 60 degrees,  hence the angles we have labeled as KRZ and RKZ both measure 1 half of 180 minus 60 minus 70 degrees or 1 half of 50 degrees  or they both measure 25 degrees each. And then we're almost done.  We know that the angle MKZ being  in the equilateral triangle measures 60 degrees. So the angle we're looking for, RKM, measures the difference 60 minus 25 degrees or 35 degrees. And so the answer is D.

Video Summary

The problem involves determining the measure of angle RKM after an equilateral triangle KZM is rotated 130 degrees clockwise to become triangle RZT. Angle RKM, using properties of isosceles and equilateral triangles, is calculated by subtracting the 25-degree angles from the 60-degree angle of the original equilateral triangle KZM. The triangle's symmetry indicates angles KRZ and RKZ both measure 25 degrees. Hence, angle RKM equals 60 degrees minus 25 degrees, resulting in 35 degrees. The correct answer is option D, 35 degrees.

Keywords

equilateral triangle

angle calculation

triangle rotation

isosceles triangle

geometry problem