Datuenso554idn
Answered

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The ratio of the angles of a 180 degrees triangle is 3:4:5. Find the measure of each angle​

Sagot :

KAntoineDoixidn

✒️RATIO

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[tex] \large\underline{\mathbb{PROBLEM}:} [/tex]

  • The ratio of the angles of a 180 degrees triangle is 3:4:5. Find the measure of each angle.

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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \Large \: \rm{45\degree, \,60\degree, \: and \:\: 75\degree} [/tex]

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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

» Let x be the number multiplied to each part of the ratio that adds up to 180°

  • [tex] 3x + 4x + 5x = 180 \degree [/tex]

  • [tex] 12x = 180 \degree [/tex]

  • [tex] \frac{12x}{12} = \frac{180\degree}{12} \\ [/tex]

  • [tex] x = 15\degree [/tex]

» Multiply the value of x to each part of the ratio to find the measure of each angle.

  • [tex] 3x \::\: 4x \::\: 5x [/tex]

  • [tex] 3(15\degree) \::\: 4(15\degree) \::\: 5(15\degree) [/tex]

  • [tex] 45\degree \::\: 60\degree \::\: 75\degree [/tex]

[tex] \therefore [/tex] The measure of each angle is 45°, 60°, and 75°

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