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$In /_\JKL,m/_J=(5x+1)^(@),m/_K=(x+14)^(@), and m/_L=(3x+12)^(@). What is the value of x ? Answer:$

In $\triangle \mathrm{JKL}, \mathrm{m} \angle J=(5 x+1)^{\circ}, \mathrm{m} \angle K=(x+14)^{\circ}$ , and $\mathrm{m} \angle L=(3 x+12)^{\circ}$ . What is the value of $x$ ? $\newline$ Answer:

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Find trigonometric functions using a calculator

Full solution

Q. In

\triangle \mathrm{JKL}, \mathrm{m} \angle J=(5 x+1)^{\circ}, \mathrm{m} \angle K=(x+14)^{\circ}

, and

\mathrm{m} \angle L=(3 x+12)^{\circ}

. What is the value of

x

?

\newline

Answer:

Write Equation: Since triangle JKL is a triangle, the sum of its angles must be $180$ degrees. So, we can write the equation: $\newline$ $(5x + 1) + (x + 14) + (3x + 12) = 180$
Add Terms: Now, let's add up all the $x$ terms and the constant terms: $5x + x + 3x + 1 + 14 + 12 = 180$
Combine Like Terms: Combining like terms gives us: $9x + 27 = 180$
Isolate $x$ Term: Subtract $27$ from both sides to isolate the term with $x$ : $9x = 180 - 27$
Subtraction: Now, let's do the subtraction: $9x = 153$
Divide to Solve: Finally, divide both sides by $9$ to solve for $x$ : $x = \frac{153}{9}$
Divide to Solve: Finally, divide both sides by $9$ to solve for $x$ : $x = \frac{153}{9}$ And here's the division: $x = 17$

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