Question 1102152
.
One of the same side angles of two parallel lines is three times the other angle. Find all angles.
~~~~~~~~~~~~~~~~~


<pre>
The same side angles at two parallel lines and a transverse are EITHER supplementary (when they sum up to 180 degs),  OR  congruent.


In your case the angles are different, so they are supplementary.


Let x be the measure of one angle; then the other is 3x.


They sum up to 180:  x + 3x = 180  ====>  4x = 180  ====>  x = {{{180/4}}} = 45.


<U>Answer</U>.  The angles are 45 degs and 135 degs.
</pre>

On parallel lines and the angles formed at a transverse line see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Angles/Parallel-lines.lesson>Parallel lines</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/How-to-solve-problems-on-parallel-lines-Examples.lesson>HOW TO solve problems on parallel lines - Examples</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lesson is the part of this online textbook under the topic 
"<U>Basics of angles. Supplementary, complementary angles. Vertical angles. Parallel lines</U>".


Save the link to this online textbook together with its description


Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson


to your archive and use it when it is needed.