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.

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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

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1 Answer
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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.