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In /_\STU,m/_S=(4x+6)^(@),m/_T=(4x-1)^(@), and m/_U=(x+4)^(@). What is the value of x ? Answer:

In △STU,m∠S=(4x+6)∘,m∠T=(4x−1)∘ \triangle \mathrm{STU}, \mathrm{m} \angle S=(4 x+6)^{\circ}, \mathrm{m} \angle T=(4 x-1)^{\circ} , and m∠U=(x+4)∘ \mathrm{m} \angle U=(x+4)^{\circ} . What is the value of x x ?\newlineAnswer:

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Full solution

Q. In △STU,m∠S=(4x+6)∘,m∠T=(4x−1)∘ \triangle \mathrm{STU}, \mathrm{m} \angle S=(4 x+6)^{\circ}, \mathrm{m} \angle T=(4 x-1)^{\circ} , and m∠U=(x+4)∘ \mathrm{m} \angle U=(x+4)^{\circ} . What is the value of x x ?\newlineAnswer:
  1. Triangle Angle Sum Equation: The sum of the angles in any triangle is 180180 degrees. We can set up an equation with the given angle measures to find the value of xx.
  2. Add Angle Measures: Let's add up the measures of the angles and set them equal to 180180 degrees:\newline(4x+6)∘+(4x−1)∘+(x+4)∘=180∘(4x + 6)^\circ + (4x - 1)^\circ + (x + 4)^\circ = 180^\circ.
  3. Combine Like Terms: Combine like terms: 4x+4x+x+6−1+4=1804x + 4x + x + 6 - 1 + 4 = 180.
  4. Simplify Equation: This simplifies to: 9x+9=1809x + 9 = 180.
  5. Isolate x Term: Subtract 99 from both sides to isolate the term with xx: 9x=1719x = 171.
  6. Solve for x: Divide both sides by 99 to solve for x:\newlinex=1719x = \frac{171}{9}.
  7. Calculate x Value: Calculate the value of x:\newlinex=19x = 19.

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