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In /_\ HIJ, m/_H=(6x+8)^(@),m/_I=(x+4)^(@), and m/_J=(5x+12)^(@). Find m/_I. Answer:

In △ \triangle HIJ, m∠H=(6x+8)∘,m∠I=(x+4)∘ \mathrm{m} \angle H=(6 x+8)^{\circ}, \mathrm{m} \angle I=(x+4)^{\circ} , and m∠J=(5x+12)∘ \mathrm{m} \angle J=(5 x+12)^{\circ} . Find m∠I \mathrm{m} \angle I .\newlineAnswer:

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Full solution

Q. In △ \triangle HIJ, m∠H=(6x+8)∘,m∠I=(x+4)∘ \mathrm{m} \angle H=(6 x+8)^{\circ}, \mathrm{m} \angle I=(x+4)^{\circ} , and m∠J=(5x+12)∘ \mathrm{m} \angle J=(5 x+12)^{\circ} . Find m∠I \mathrm{m} \angle I .\newlineAnswer:
  1. Identify Relationship: Identify the relationship between the angles in a triangle.\newlineThe sum of the angles in any triangle is 180180 degrees.
  2. Set Up Equation: Set up the equation using the given angle expressions.\newlinem/_H+m/_I+m/_J=180m/\_H + m/\_I + m/\_J = 180 degrees\newline(6x+8)+(x+4)+(5x+12)=180(6x+8) + (x+4) + (5x+12) = 180
  3. Combine Like Terms: Combine like terms in the equation.\newline6x+x+5x+8+4+12=1806x + x + 5x + 8 + 4 + 12 = 180\newline12x+24=18012x + 24 = 180
  4. Solve for x: Solve for x.\newlineSubtract 2424 from both sides of the equation.\newline12x+24−24=180−2412x + 24 - 24 = 180 - 24\newline12x=15612x = 156
  5. Divide and Find x: Divide both sides by 1212 to find the value of x.\newline12x12=15612\frac{12x}{12} = \frac{156}{12}\newlinex=13x = 13
  6. Substitute x Value: Substitute the value of xx back into the expression for m/Im/_{I}.m/I=(x+4)m/_{I} = (x + 4)m/I=(13+4)m/_{I} = (13 + 4)m/I=17m/_{I} = 17

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