Geometric discussion

He from US.
🤣
He once told me that.
I just saw @thecosmos000 use India flag on profile and I'm not sure this is him or not.

Problem 8:
ΔABC is a triangle. D, E are points on BC, AC respectively such that AB=AD and EC=ED. If ∠ADE=65° and ∠DEC=90° Find the size of ∠BAC.

Problem 9:
Given a triangle whose 3 adjacent angle on the line of interior are 4x, 5x, and 6x.
Find the value of x.

Problem 10:
ΔABC is a triangle. D,G are points on AB such that AD=DG=GB and E,F are points on AC such that AE=EF=FC. if the area of □DEFG is 30 cm².
Find the area of ΔABC.

65°
Correct!
∠ECD=∠EDC=45°
∠ABD=∠ADC=180°-45°-65°=70°
∠BAC =180°-∠ABC-∠ACB=180°-45°-70°= 65°

AD:AG = AE:EF = 1:2
∠DAE = ∠GAF (joint angle)
So ΔADE ~ ΔAGF
In the same way we can prove that ΔADE ~ ΔABC
Then the area ratio of two similar triangles is equal to the square of the side length ratio.
He from US.