Math, asked by brajeshkumar111, 19 days ago

The measure of three angles of triangle are 3x-17, x+40, 2x-5. Find x​

Answers

Answered by ItzBrainlyLords
1

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 \large \sf \star \underline{ \red{ \: solution : }} \\

  • Angle Sum Property

Sum of all 3 interior angles = 180°

Angles :

  • 3x - 17
  • x + 40
  • 2x - 5

Solving :

 \\   \large\tt \implies \: 3x - 17 + x + 40 + 2x - 5 = 180 \degree \\  \\  \large  \tt \implies \: 6x  + 18= 180 \degree \\  \\ \large  \tt \implies \: 6x  = 180 \degree  - 18\\  \\ \large  \tt \implies \: 6x   = 162 \degree \\  \\  \large \tt \implies \: x =  \frac{162 \degree}{6}  \\  \\  \large \looparrowright \:  \underline{ \boxed{ \green{ \sf \: x = 27 \degree}}} \\

For Angles :

➢ 3x - 17 = 3(27) - 17

⇒ 81 - 17

  • 1 angle = 64°

➢ x + 40 = 27 + 40

  • 2 angle = 67°

➢ 2x - 5 = 2(27) - 5

⇒ 54 - 5

  • 3 angle = 49°

Check :

  • Angle Sum Property

⇒ 1 angle + 2 angle + 3 angle = 180°

⇒ 64° + 67° + 49° = 180°

Therefore, 180° = 180°

Hence Proved

  • Value of x = 27°
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