angles exercise
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http://prntscr.com/9f1imw i already know a and b btw
well i added more problems in one, because they are kinda same topic.
well i added more problems in one, because they are kinda same topic.
For problem (c):
Look at triangle IJK. You know that \(\displaystyle \angle LKI\) and \(\displaystyle \angle IKJ\) together form a straight line, so what must be the measure of \(\displaystyle \angle IKJ\)? Similarly, \(\displaystyle \angle HIK\) and \(\displaystyle \angle JIK\) also form a straight line. So what must be the measure of \(\displaystyle \angle JIK\)? Then you know two angles of the triangle IJK, so what must be the measure of the remaining third angle, \(\displaystyle \angle IJK\)?
You also know that in the quadrilateral HIKL, all four points lie on the circumference of the circle. Based on this information, what can you say about the opposite angles of this quadrilateral? Given that fact, what must be the measure of \(\displaystyle \angle HLK\)? Then note that \(\displaystyle \angle HLK\) and \(\displaystyle \angle KLM\) form a straight line. So what must be the measure of \(\displaystyle \angle KLM\)?
Then you can apply similar reasoning to the other problems. If you get stuck again, that's okay, but when you reply back, please include all of your work so far, even if you know it's wrong. Thank you.
Look at triangle IJK. You know that \(\displaystyle \angle LKI\) and \(\displaystyle \angle IKJ\) together form a straight line, so what must be the measure of \(\displaystyle \angle IKJ\)? Similarly, \(\displaystyle \angle HIK\) and \(\displaystyle \angle JIK\) also form a straight line. So what must be the measure of \(\displaystyle \angle JIK\)? Then you know two angles of the triangle IJK, so what must be the measure of the remaining third angle, \(\displaystyle \angle IJK\)?
You also know that in the quadrilateral HIKL, all four points lie on the circumference of the circle. Based on this information, what can you say about the opposite angles of this quadrilateral? Given that fact, what must be the measure of \(\displaystyle \angle HLK\)? Then note that \(\displaystyle \angle HLK\) and \(\displaystyle \angle KLM\) form a straight line. So what must be the measure of \(\displaystyle \angle KLM\)?
Then you can apply similar reasoning to the other problems. If you get stuck again, that's okay, but when you reply back, please include all of your work so far, even if you know it's wrong. Thank you.
So i have done the IJK in example c , just how you said it, but i don't understand how do i get the number of HLK , i know that KLM will be 180-HLK .
You can find \(\displaystyle \angle HLK\) because it is part of a quadrilateral where all four points are on the same circle. So, the opposite angles of that quadrilateral must add up to 180. Then, note that \(\displaystyle \angle HLK\) is opposite \(\displaystyle \angle HIK\), whose measure you do know.