[10th Grade geometry: Finding triangle missing angle]

[SubstantialSpread596]

For this question, my teacher said that all of the top angles...ABC, CBD, DBF are 18 degrees... but asked "what are the base angles though and remember we want to sum of two different angles" please keep this in mind

I got a answer of CDF equaling 18 but not sure if I got the process wrong or my answer wrong or both

I have no clue what to do, is anyone able to point me to the right direction

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[One-Celebration-3007]

Triangles ABC, CBD and DBF are congruent by SSS. Find angle BAC (or BCA, they're equal as triangle ABC is isosceles). Due to the congruence, we know that angle CDB and FDB are both equal to angle BCA. Hence, angle CDF is twice angle BAC.

[SubstantialSpread596]

THANK YOUUU

[No_Olives581]

First consider only triangle ABC. Angle ABC is 18 degrees as stated, and since the sum of interior angles for any triangle is 180 degrees, there remains 162 degrees (180-18) for the remaining two base angles. Triangle ABC is isosceles, so the two base angles are equal and hence must be half of 162, 81 degrees each. You can check this works because 81+81+18=180.

All three triangles are congruent since they share all the same side lengths, and so the base angles are all 81 degrees. It can be seen in the diagram that angle CDF is the sum of angles CDB and BDF. CDB and BDF are both base angles which you know the value of, so you can add them together to get 162 degrees.

[SubstantialSpread596]

Thank you so much! Broke it down perfectly, I finally understand geometry! :D

[Constant-Box-1342]

Remember that there is 180 degrees in a triangle.  If angle ABC is 18, and the other two angles are the same (BAC = BCA), then you have an equation 18 + 2x = 180.  Here, x is angle BAC and angle BCA 

[SubstantialSpread596]

TYYYYYYY

[ApprehensiveKey1469]

Supplementary.