Triangle DEF is specified. Angle D is less than angle F by 40 °, and angle E is 3 times less than angle B.

Triangle DEF is specified. Angle D is less than angle F by 40 °, and angle E is 3 times less than angle B. Find all the corners of the triangle. Which side is bigger than DE or EF?

Let the value of the angle DFE = X0, then, by condition, the angle FDE = (X – 40) 0, the angle DEF = DEF / 3 = (X – 40) / 3.

The sum of the interior angles of the triangle is 180, then (X + (X – 40) + (X – 40) / 3) = 180.

3 * X + 3 * X – 120 + X – 40 = 3 * 180.

7 * X = 540 + 40 + 120 = 70.

X = EFD = 700/7 = 100.

Then the angle FDE = 100 – 40 = 60, the angle DEF = 60/3 = 20.

The DE side is opposite the largest angle, then DE> EF.

Answer: The angles of the triangle are 100, 60, 20, side DE> EF.