What is the measure of angle F? This is an isosceles triangle with base angles being the only part filled in. I have trouble understanding that if the base angles are not like terms, then how can I solve my equation (which is angle measure D equals angle measure E)? Help? This is my triangle. Also, I checked in the back of my math book and it told me the correct answers were either 130 degrees or 172 degrees, but I still don't understand how they came about these answers.

Base angles of an isoceles triangle are congruent. Therefore you get $x^2=3x+10$, which simplifies to $x^2-3x-10=0$ which after factoring yields the possibilities $x=5$ or $x=-2$, which both work. 
If you plug in $x=5$, you will get that the base angles are both $25$ degrees, which means the missing angle is $150$ degrees. 
If you plug in $x=-2$, you will get that the base angles are both $4$ degrees, which means that the missing angle is $172$ degrees.
