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.




Those 130 and 172 degrees are possibilities for the top angle, not the base angles. (And WHY couldn’t these figures be used for the base angles?)
– imranfat
Oct 21 at 2:09



Can you rotate your image so people can read it without turning their heads and reupload it?
– suomynonA
Oct 21 at 2:11


1 Answer


Base angles of an isoceles triangle are congruent. Therefore you get x2=3x+10x^2=3x+10, which simplifies to x2−3x−10=0x^2-3x-10=0 which after factoring yields the possibilities x=5x=5 or x=−2x=-2, which both work.

If you plug in x=5x=5, you will get that the base angles are both 2525 degrees, which means the missing angle is 150150 degrees.

If you plug in x=−2x=-2, you will get that the base angles are both 44 degrees, which means that the missing angle is 172172 degrees.