Solving for an Unknown Involving Triangles

In triangles the total sum of the degrees is 180.  However, it is also true that any exterior angle of a triangle, will equal the sum of the two interior angles to which it isn’t adjacent to.  We can use this rule to help solve adjacent angles much quicker than solving the third angle of a triangle and then using a straight angle rule.

First try to solve for an unknown, x, where you are only working with solving a single interior angle.

Now we can solve for an unknown, x, where you are only working with interior angles.  Remember that even if multiple angles are variables that we can still set the sum of all of the angles to 180 and then solve the equation for x.

Next try to solve for an unknown, x, where we have introduced an exterior angle.

This style of problem is still solving for an unknown, x, where we have introduced an exterior angle.  However, in this situation you will have to do a little more algebra in order to get your final answer.

If you are looking for additional practice beyond this, there is a printable worksheet.