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In /_\DEF,m/_D=(10 x-13)^(@),m/_E=(x-4)^(@), and m/_F=(2x+15)^(@). Find m/_E. Answer:

In △DEF,m∠D=(10x−13)∘,m∠E=(x−4)∘ \triangle \mathrm{DEF}, \mathrm{m} \angle D=(10 x-13)^{\circ}, \mathrm{m} \angle E=(x-4)^{\circ} , and m∠F=(2x+15)∘ \mathrm{m} \angle F=(2 x+15)^{\circ} . Find m∠E \mathrm{m} \angle E .\newlineAnswer:

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Q. In △DEF,m∠D=(10x−13)∘,m∠E=(x−4)∘ \triangle \mathrm{DEF}, \mathrm{m} \angle D=(10 x-13)^{\circ}, \mathrm{m} \angle E=(x-4)^{\circ} , and m∠F=(2x+15)∘ \mathrm{m} \angle F=(2 x+15)^{\circ} . Find m∠E \mathrm{m} \angle E .\newlineAnswer:
  1. Recognize Triangle Angle Sum: Recognize that the sum of the angles in any triangle is 180180 degrees.\newlineUsing the angle sum property of triangles: \newlinem/_D+m/_E+m/_F=180m/\_D + m/\_E + m/\_F = 180 degrees
  2. Substitute Given Expressions: Substitute the given expressions for m/Dm/_{D}, m/Em/_{E}, and m/Fm/_{F} into the angle sum equation.\newline(10x−13)+(x−4)+(2x+15)=180(10x - 13) + (x - 4) + (2x + 15) = 180
  3. Combine Like Terms: Combine like terms on the left side of the equation.\newline10x−13+x−4+2x+15=18010x - 13 + x - 4 + 2x + 15 = 180\newline13x−2=18013x - 2 = 180
  4. Add to Isolate Terms: Add 22 to both sides of the equation to isolate the terms with xx on one side.\newline13x−2+2=180+213x - 2 + 2 = 180 + 2\newline13x=18213x = 182
  5. Divide to Solve for x: Divide both sides of the equation by 1313 to solve for x.\newline13x13=18213\frac{13x}{13} = \frac{182}{13}\newlinex=14x = 14
  6. Substitute Value of xx: Substitute the value of xx back into the expression for m/_Em/\_E to find the measure of angle E.\newlinem/_E=(x−4)m/\_E = (x - 4) degrees\newlinem/_E=(14−4)m/\_E = (14 - 4) degrees\newlinem/_E=10m/\_E = 10 degrees

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