Question

John is building a doghouse. He decides to use the roof truss design shown. If m/DBF = 35°, what is the measure of the vertex angle of the isosceles triangle?

Answer 1

Check the picture below.

so we can say that the angles at vertex B are linear angles and thus they add up to 180°.

`35 + 90 + (2x + 15) ~~ = ~~180\implies 2x+140=180\implies 2x=40 \\\\\\ x=\cfrac{40}{2}\implies \boxed{x=20} \\\\[-0.35em] ~\dotfill\\\\ \measuredangle ABC ~~ = ~~ \measuredangle ACB =2x+15 \implies 2(20)+15\implies 55^o \\\\\\ \measuredangle ABC + \measuredangle ACB +y=180\implies 55+55+y=180 \\\\\\ 110+y=180\implies \boxed{y=70^o}`