/_1 and /_2 are vertical angles. If m/_1=(2x+30)^(@) and m/_2=(3x-10)^(@), then find the measure of /_1. Answer:

Vertical Angles Congruent: Vertical angles are congruent, which means they have the same measure. Therefore, we can set the expressions for m/angle 1 and m/angle 2 equal to each other to find the value of x. (2x + 30) = (3x - 10)Solve for x: Now, we solve for x by subtracting 2x from both sides of the equation. (2x + 30) - 2x = (3x - 10) - 2x 30 = x - 10Isolate x: Next, we add 10 to both sides of the equation to isolate x. 30 + 10 = x - 10 + 10 40 = xSubstitute x into Angle 1: Now that we have the value of x, we can substitute it back into the expression for m/angle 1 to find the measure of angle 1. m/angle 1 = 2x + 30 m/angle 1 = 2(40) + 30Find Measure of Angle 1: Finally, we perform the multiplication and addition to find the measure of angle 1. m/angle 1 = 80 + 30 m/angle 1 = 110 degrees

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Full solution

\angle 1

and

\angle 2

are vertical angles. If

\mathrm{m} \angle 1=(2 x+30)^{\circ}

and

\mathrm{m} \angle 2=(3 x-10)^{\circ}

, then find the measure of

\angle 1

\newline

Answer:

Vertical Angles Congruent: Vertical angles are congruent, which means they have the same measure. Therefore, we can set the expressions for $m/\text{angle } 1$ and $m/\text{angle } 2$ equal to each other to find the value of $x$ . $\$2x + 30$ = $3x - 10$ \)
Solve for x: Now, we solve for x by subtracting $2x$ from both sides of the equation. $\newline$ $(2x + 30) - 2x = (3x - 10) - 2x$ $\newline$ $30 = x - 10$
Isolate x: Next, we add $10$ to both sides of the equation to isolate $x$ . $\newline$ $30 + 10 = x - 10 + 10$ $\newline$ $40 = x$
Substitute $x$ into Angle $1$ : Now that we have the value of $x$ , we can substitute it back into the expression for $m/\text{angle } 1$ to find the measure of angle $1$ . $\newline$ $m/\text{angle } 1 = 2x + 30$ $\newline$ $m/\text{angle } 1 = 2(40) + 30$
Find Measure of Angle $1$ : Finally, we perform the multiplication and addition to find the measure of angle $1$ . $\newline$ m/angle $1$ = $80 + 30$ $\newline$ m/angle $1$ = $110$ degrees