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$In /_\CDE,m/_C=(8x+19)^(@),m/_D=(2x+7)^(@), and m/_E=(4x-14)^(@). What is the value of x ? Answer:$

In $\triangle \mathrm{CDE}, \mathrm{m} \angle C=(8 x+19)^{\circ}, \mathrm{m} \angle D=(2 x+7)^{\circ}$ , and $\mathrm{m} \angle E=(4 x-14)^{\circ}$ . What is the value of $x$ ? $\newline$ Answer:

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Csc, sec, and cot of special angles

Full solution

Q. In

\triangle \mathrm{CDE}, \mathrm{m} \angle C=(8 x+19)^{\circ}, \mathrm{m} \angle D=(2 x+7)^{\circ}

, and

\mathrm{m} \angle E=(4 x-14)^{\circ}

. What is the value of

x

?

\newline

Answer:

Write Triangle Angle Equation: The sum of the angles in any triangle is $180$ degrees. We can write this as an equation using the given angle measures: $\newline$ $m/\_C + m/\_D + m/\_E = 180^\circ$ $\newline$ $(8x + 19)^\circ + (2x + 7)^\circ + (4x - 14)^\circ = 180^\circ$
Simplify Equation: Combine like terms to simplify the equation: $\newline$ $8x + 2x + 4x + 19 + 7 - 14 = 180$ $\newline$ $14x + 12 = 180$
Isolate x Term: Subtract $12$ from both sides to isolate the term with $x$ : $\newline$ $14x + 12 - 12 = 180 - 12$ $\newline$ $14x = 168$
Solve for x: Divide both sides by $14$ to solve for x: $\newline$ $\frac{14x}{14} = \frac{168}{14}$ $\newline$ $x = 12$

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