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The measures of the three angles of a
triangle are given by 2x + 6, x, and 3x.
What is the measure of the largest angle?

Sagot :

Sarah06109idn

Answer:

[tex]\boxed {\boxed {\sf 87 \ degrees}}[/tex]

Step-by-step explanation:

The angles in a triangle must add to 180 degrees.

We are given three angles: 2x+6, x, and 3x. Their sum must be 180, so we can create an equation.

[tex]2x+6+x+3x=180[/tex]

Combine like terms (all terms with an x) on the left side.

[tex](2x+x+3x)+6=180[/tex]

[tex]6x+6=180[/tex]

Now solve for x by isolating the variable.

6 is being added and the inverse of addition is subtraction. Subtract 6 from both sides.

[tex]6x+6-6=180-6\\6x=174\\[/tex]

x is being multiplied by 6. The inverse of multiplication is division. Divide both sides by 6.

[tex]6x/6=174/6 \\x=29[/tex]

Substitute 29 for x in the angle measures.

  • 2x+6= 2(29)+6=58+6=64
  • x=29
  • 3x= 3(29)=87

The largest angle is 87 degrees.

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