Question 1093916
.
The measure of each of the base angles of an isosceles triangle is 24 degrees less than the measure of the vertex angle. 
Find the measure of the vertex angle.
~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let x be the measure of the vertex angle in degrees.

Then the measure of each base angle is (x-24) degrees.


Your equation is

x + (x-24) + (x-24) = 180,

3x - 48 = 180  ====>  3x = 180 + 48  ====>  x = 76 degrees.
</pre>

<U>Answer</U>.  The vertex angle is of 76 degrees.



------------
See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-angles-of-a-triangle.lesson>Solved problems on angles of a triangle</A>

in this site.


You will find there many samples of similar solved problems.


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 &nbsp;"<U>Finding angles of triangles, parallelograms and rectangles</U>".



=============
Be aware: &nbsp;&nbsp;the solution by @josgatithmetic is &nbsp;<U>W R O N G</U>. 


Simply ignore it . . .