in a triangle DEF m<E is three times m<,and m <F is 9 less than m< E
D = X deg.
E = 3X,
F = 3X - 9.
X + 3X + (3X - 9) = 180deg.
7X = 180 + 9,
7X = 189,
X = 189 / 7 = 27deg.
D = X = 27deg.
E = 3X = 3*27 = 81deg.
F = 3X - 9 = 3*27 - 9 = 72deg.
To find the measurements of angles E, F, and D in triangle DEF, we can make use of the given information that m<E is three times m<, and m <F is 9 less than m<E.
Let's assume that the measurement of angle E is x degrees. Based on the given information, we know that angle F is 9 degrees less than angle E, so angle F is (x - 9) degrees.
Furthermore, it is given that angle E is three times angle D. We can set up an equation to represent this relationship:
x = 3 * angle D
To solve for angle D, we divide both sides of the equation by 3:
angle D = x / 3
Now we know the measurements of all three angles in terms of angle E.
Angle E = x degrees
Angle F = (x - 9) degrees
Angle D = x / 3 degrees