/_1 and /_2 are supplementary angles. If m/_1=(2x+15)^(@) and m/_2=(4x+9)^(@), then find the measure of /_1. Answer:

Set up equation: Supplementary angles add up to 180 degrees. We can set up an equation with the given expressions for m/angle 1 and m/angle 2 to find the value of x. m/angle 1 + m/angle 2 = 180° (2x + 15)° + (4x + 9)° = 180°Combine like terms: Combine like terms to simplify the equation. 2x + 4x + 15 + 9 = 180 6x + 24 = 180Isolate x: Subtract 24 from both sides to isolate the term with x. 6x + 24 - 24 = 180 - 24 6x = 156Solve for x: Divide both sides by 6 to solve for x. 6x / 6 = 156 / 6 x = 26Find angle 1: Now that we have the value of x, we can find the measure of angle 1 by substituting x back into the expression for m/angle 1. m/angle 1 = (2x + 15)° m/angle 1 = (2(26) + 15)°Calculate angle 1: Calculate the value of m/angle 1. m/angle 1 = (52 + 15)° m/angle 1 = 67°

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/_1 and
/_2 are supplementary angles. If
m/_1=(2x+15)^(@) and
m/_2=(4x+9)^(@), then find the measure of
/_1.
Answer:

$\angle 1$ and $\angle 2$ are supplementary angles. If $\mathrm{m} \angle 1=(2 x+15)^{\circ}$ and $\mathrm{m} \angle 2=(4 x+9)^{\circ}$ , then find the measure of $\angle 1$ . $\newline$ Answer:

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Math Problems

Algebra 2

Transformations of functions

Full solution

\angle 1

and

\angle 2

are supplementary angles. If

\mathrm{m} \angle 1=(2 x+15)^{\circ}

and

\mathrm{m} \angle 2=(4 x+9)^{\circ}

, then find the measure of

\angle 1

\newline

Answer:

Set up equation: Supplementary angles add up to $180$ degrees. We can set up an equation with the given expressions for $m/\text{angle } 1$ and $m/\text{angle } 2$ to find the value of $x$ . $\newline$ $m/\text{angle } 1 + m/\text{angle } 2 = 180°$ $\newline$ $(2x + 15)° + (4x + 9)° = 180°$
Combine like terms: Combine like terms to simplify the equation. $\newline$ $2x + 4x + 15 + 9 = 180$ $\newline$ $6x + 24 = 180$
Isolate x: Subtract $24$ from both sides to isolate the term with $x$ . $\newline$ $6x + 24 - 24 = 180 - 24$ $\newline$ $6x = 156$
Solve for x: Divide both sides by $6$ to solve for x. $\newline$ $\frac{6x}{6} = \frac{156}{6}$ $\newline$ $x = 26$
Find angle $1$ : Now that we have the value of $x$ , we can find the measure of angle $1$ by substituting $x$ back into the expression for $m/\text{angle } 1$ .
$m/\text{angle } 1 = (2x + 15)^\circ$
$m/\text{angle } 1 = (2(26) + 15)^\circ$
Calculate angle $1$ : Calculate the value of $m/\text{angle } 1$ . $\newline$ $m/\text{angle } 1 = (52 + 15)^\circ$ $\newline$ $m/\text{angle } 1 = 67^\circ$