Labaosamuell08idn
Answered

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Use the given information to find the values of x and y.

Use The Given Information To Find The Values Of X And Y class=

Sagot :

KAntoineDoixidn

✒️CONGRUENCE

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

[tex] \qquad \Large \:\: \rm 1) \; x = 25 \;,\; y = 2 [/tex]

[tex] \qquad \Large \:\: \rm 2) \; x = 12 \;,\; y = 6 [/tex]

*Please read and understand my solution. Don't just rely on my direct answer*

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

Number 1:

Angle B corresponds to angle M. Thus, their measures are equal. Solve for x.

  • [tex] \rm m \angle B = m\angle M [/tex]

  • [tex] 2x - 20 = 30 [/tex]

  • [tex] 2x = 30 + 20 [/tex]

  • [tex] 2x = 50 [/tex]

  • [tex] \frac{2x}2 = \frac{50}2 \\ [/tex]

  • [tex] x = 25 [/tex]

Side AC corresponds to side LN. Thus, their lengths are equal. Solve for y.

  • [tex] \rm AC = LN [/tex]

  • [tex] 15 = 3y + 9 [/tex]

  • [tex] 15-9 = 3y [/tex]

  • [tex] 6 = 3y [/tex]

  • [tex] \frac{\,6\,}3 = \frac{3y}3 \\ [/tex]

  • [tex] 2 = y [/tex]

Therefore, the value of x is 25 and the value of y is 2.

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Number 2:

Angle C corresponds to angle N. Thus, their measures are equal. Solve for x.

  • [tex] \rm m \angle C = m\angle N [/tex]

  • [tex] 67 = 5x + 7 [/tex]

  • [tex] 67 - 7 = 5x[/tex]

  • [tex] 60 = 5x [/tex]

  • [tex] \frac{60}5 = \frac{5x}5 \\ [/tex]

  • [tex] x = 12 [/tex]

Side AB corresponds to side LM. Thus, their lengths are equal. Solve for y.

  • [tex] \rm AB = LM [/tex]

  • [tex] 7y - 8 = 2y + 22 [/tex]

  • [tex] 7y - 2y = 22 + 8 [/tex]

  • [tex] 5y = 30 [/tex]

  • [tex] \frac{5y}5 = \frac{30}5 \\ [/tex]

  • [tex] y = 6 [/tex]

Therefore, the value of x is 12 and the value of 6 is 2.

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(ノ^_^)ノ [tex] \large\qquad\qquad\qquad\tt 3 /1 /2022 [/tex]