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

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Q. In △JKL,m∠J=(5x+1)∘,m∠K=(x+14)∘ \triangle \mathrm{JKL}, \mathrm{m} \angle J=(5 x+1)^{\circ}, \mathrm{m} \angle K=(x+14)^{\circ} , and m∠L=(3x+12)∘ \mathrm{m} \angle L=(3 x+12)^{\circ} . What is the value of x x ?\newlineAnswer:
  1. Write Equation: Since triangle JKL is a triangle, the sum of its angles must be 180180 degrees. So, we can write the equation:\newline(5x+1)+(x+14)+(3x+12)=180(5x + 1) + (x + 14) + (3x + 12) = 180
  2. Add Terms: Now, let's add up all the xx terms and the constant terms: 5x+x+3x+1+14+12=1805x + x + 3x + 1 + 14 + 12 = 180
  3. Combine Like Terms: Combining like terms gives us: 9x+27=1809x + 27 = 180
  4. Isolate xx Term: Subtract 2727 from both sides to isolate the term with xx:9x=180−279x = 180 - 27
  5. Subtraction: Now, let's do the subtraction: 9x=1539x = 153
  6. Divide to Solve: Finally, divide both sides by 99 to solve for xx:x=1539x = \frac{153}{9}
  7. Divide to Solve: Finally, divide both sides by 99 to solve for xx:x=1539x = \frac{153}{9} And here's the division:x=17x = 17

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