SOLUTION: In a triangle DEF, m〈E is three times m 〈D, and m〈F is 9 less than m〈E. What is the measure of each angle? Thank u

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Question 982145: In a triangle DEF, m〈E is three times m 〈D, and m〈F is 9 less than m〈E. What is the measure of each angle? Thank u
Answer by ikleyn(52825) About Me  (Show Source):
You can put this solution on YOUR website!

Let  x  be the measure of the angle  LD:   x = m(LD)  (in degrees).

Then the measure of the angle  LE  be  3x,  and the measure of the angle  LF  be  3x - 9°  degrees.

Since the sum of interior angles of a triangle is equal to 180°,  you have an equation

x + 3x + (3x - 9) = 180.

Simplify and solve it:

7x - 9 = 180,

7x = 180 + 9,

7x = 189,

x = 189%2F7 = 27°.

Hence,  m(LD) = 27°,  m(LE) = 3*27° = 81°, and  m(LE) = 81° - 9° = 72°.