/_1 and /_2 are vertical angles. If m/_1=(x+18)^(@) and m/_2=(4x-24)^(@), then find the measure of /_1. Answer:

Vertical angles congruent: Vertical angles are congruent, so their measures are equal. We can set the expressions for the measures of angle 1 and angle 2 equal to each other to find the value of x. m/∠1 = m/∠2 (x + 18)° = (4x - 24)°Set expressions equal: Solve the equation for x by first subtracting x from both sides to get the x terms on one side. (4x - 24)° - x = (x + 18)° - x 3x - 24 = 18Solve for x: Next, add 24 to both sides to isolate the term with x. 3x - 24 + 24 = 18 + 24 3x = 42Isolate x term: Divide both sides by 3 to solve for x. 3x / 3 = 42 / 3 x = 14Substitute x value: Now that we have the value of x, we can substitute it back into the expression for m/∠1 to find the measure of angle 1. m/∠1 = (x + 18)° m/∠1 = (14 + 18)° m/∠1 = 32°

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/_1 and
/_2 are vertical angles. If
m/_1=(x+18)^(@) and
m/_2=(4x-24)^(@), then find the measure of
/_1.
Answer:

$\angle 1$ and $\angle 2$ are vertical angles. If $\mathrm{m} \angle 1=(x+18)^{\circ}$ and $\mathrm{m} \angle 2=(4 x-24)^{\circ}$ , then find the measure of $\angle 1$ . $\newline$ Answer:

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Full solution

\angle 1

and

\angle 2

are vertical angles. If

\mathrm{m} \angle 1=(x+18)^{\circ}

and

\mathrm{m} \angle 2=(4 x-24)^{\circ}

, then find the measure of

\angle 1

\newline

Answer:

Vertical angles congruent: Vertical angles are congruent, so their measures are equal. We can set the expressions for the measures of angle $1$ and angle $2$ equal to each other to find the value of $x$ . $m/\angle1 = m/\angle2$ $(x + 18)^\circ = (4x - 24)^\circ$
Set expressions equal: Solve the equation for $x$ by first subtracting $x$ from both sides to get the $x$ terms on one side. $\newline$ $(4x - 24)^\circ - x = (x + 18)^\circ - x$ $\newline$ $3x - 24 = 18$
Solve for x: Next, add $24$ to both sides to isolate the term with $x$ . $\newline$ $3x - 24 + 24 = 18 + 24$ $\newline$ $3x = 42$
Isolate x term: Divide both sides by $3$ to solve for x. $\newline$ $\frac{3x}{3} = \frac{42}{3}$ $\newline$ $x = 14$
Substitute x value: Now that we have the value of $x$ , we can substitute it back into the expression for $m/\angle1$ to find the measure of angle $1$ . $\newline$ $m/\angle1 = (x + 18)^\circ$ $\newline$ $m/\angle1 = (14 + 18)^\circ$ $\newline$ $m/\angle1 = 32^\circ$