In /_\GHI,m/_G=(5x+17)^(@),m/_H=(4x-10)^(@), and m/_I=(3x+5)^(@). Find m/_G. Answer:

Triangle Angle Sum Property: In triangle GHI, the sum of the angles must equal 180 degrees because it is a property of all triangles. We can write this as an equation: m/_G + m/_H + m/_I = 180^(@) Substitute the given expressions for m/_G, m/_H, and m/_I: (5x+17)^(@) + (4x-10)^(@) + (3x+5)^(@) = 180^(@)Combine Like Terms: Combine like terms to simplify the equation: 5x + 17 + 4x - 10 + 3x + 5 = 180 5x + 4x + 3x + 17 - 10 + 5 = 180 12x + 12 = 180Isolate x Term: Subtract 12 from both sides to isolate the term with x: 12x + 12 - 12 = 180 - 12 12x = 168Solve for x: Divide both sides by 12 to solve for x: 12x / 12 = 168 / 12 x = 14Find Angle G: Now that we have the value of x, we can find m/_G by substituting x back into the expression for m/_G: m/_G = (5x+17)^(@) m/_G = (5(14)+17)^(@) m/_G = (70+17)^(@) m/_G = 87^(@)

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Find derivatives of using multiple formulae

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Q. In

\triangle \mathrm{GHI}, \mathrm{m} \angle G=(5 x+17)^{\circ}, \mathrm{m} \angle H=(4 x-10)^{\circ}

, and

\mathrm{m} \angle I=(3 x+5)^{\circ}

\newline

Find

\mathrm{m} \angle G

\newline

Answer:

Triangle Angle Sum Property: In triangle GHI, the sum of the angles must equal $180$ degrees because it is a property of all triangles. We can write this as an equation: $\newline$ $m/_{G} + m/_{H} + m/_{I} = 180^{\circ}$ $\newline$ Substitute the given expressions for $m/_{G}$ , $m/_{H}$ , and $m/_{I}$ : $\newline$ $(5x+17)^{\circ} + (4x-10)^{\circ} + (3x+5)^{\circ} = 180^{\circ}$
Combine Like Terms: Combine like terms to simplify the equation: $\newline$ $5x + 17 + 4x - 10 + 3x + 5 = 180$ $\newline$ $5x + 4x + 3x + 17 - 10 + 5 = 180$ $\newline$ $12x + 12 = 180$
Isolate x Term: Subtract $12$ from both sides to isolate the term with $x$ : $\newline$ $12x + 12 - 12 = 180 - 12$ $\newline$ $12x = 168$
Solve for x: Divide both sides by $12$ to solve for x: $\newline$ $\frac{12x}{12} = \frac{168}{12}$ $\newline$ $x = 14$
Find Angle G: Now that we have the value of $x$ , we can find $m/\_G$ by substituting $x$ back into the expression for $m/\_G$ :
$m/\_G = (5x+17)^{@}$
$m/\_G = (5(14)+17)^{@}$
$m/\_G = (70+17)^{@}$
$m/\_G = 87^{@}$