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/_1 and
/_2 are supplementary angles. If
m/_1=(2x+21)^(@) and
m/_2=(3x+24)^(@), then find the measure of
/_1.
Answer:

$\angle 1$ and $\angle 2$ are supplementary angles. If $\mathrm{m} \angle 1=(2 x+21)^{\circ}$ and $\mathrm{m} \angle 2=(3 x+24)^{\circ}$ , then find the measure of $\angle 1$ . $\newline$ Answer:

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Transformations of functions

Full solution

Q.

\angle 1

and

\angle 2

are supplementary angles. If

\mathrm{m} \angle 1=(2 x+21)^{\circ}

and

\mathrm{m} \angle 2=(3 x+24)^{\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 $x$ . $\newline$ Calculation: $(2x + 21) + (3x + 24) = 180$
Simplify equation: Combine like terms to simplify the equation. $\newline$ Calculation: $2x + 3x + 21 + 24 = 180$ $\newline$ $5x + 45 = 180$
Isolate x: Subtract $45$ from both sides to isolate the term with $x$ . $\newline$ Calculation: $5x + 45 - 45 = 180 - 45$ $\newline$ $5x = 135$
Solve for x: Divide both sides by $5$ to solve for x. $\newline$ Calculation: $\frac{5x}{5} = \frac{135}{5}$ $\newline$ $x = 27$
Find angle measure: Now that we have the value of $x$ , we can find the measure of angle $1$ by substituting $x$ back into the expression for $m/\text{angle } 1$ . $\newline$ Calculation: $m/\text{angle } 1 = 2x + 21$ $\newline$ $m/\text{angle } 1 = 2(27) + 21$ $\newline$ $m/\text{angle } 1 = 54 + 21$ $\newline$ $m/\text{angle } 1 = 75$ degrees

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