QuestionFind $m \angle 2$ if $\angle 1$ and $\angle 2$ are vertical angles with $m \angle 1=17 x+1$ and $m \angle 2=20 x-14$ .

Studdy Solution

STEP 1

Assumptions1. $\angle1$ and $\angle$ are vertical angles. The measure of $\angle1$ is given by the expression $17x +1$
3. The measure of $\angle$ is given by the expression $20x -14$
4. Vertical angles are equal in measure

STEP 2

Since $\angle1$ and $\angle2$ are vertical angles, they are equal in measure. We can set the expressions for the measures of the two angles equal to each other and solve for $x$ .
$m \angle1 = m \angle2$

STEP 3

Substitute the given expressions for the measures of the angles into the equation.
$17x +1 =20x -14$

STEP 4

To solve for $x$ , we first need to get all terms involving $x$ on one side of the equation and the constants on the other side. We can do this by subtracting $17x$ from both sides of the equation.
$17x -17x +1 =20x -17x -14$

STEP 5

implify the equation.
$1 =3x -14$

STEP 6

Next, add14 to both sides of the equation to isolate the term with $x$ .
$1 +14 =3x -14 +14$

STEP 7

implify the equation.
$15 =3x$

STEP 8

Finally, divide both sides of the equation by3 to solve for $x$ .
$x = \frac{15}{3}$

STEP 9

implify the right side of the equation to find the value of $x$ .
$x =5$

STEP 10

Now that we know $x =5$ , we can substitute this value into the expression for $m \angle2$ to find the measure of $\angle2$ .
$m \angle2 =20x -14$

STEP 11

Substitute $x =5$ into the equation.
$m \angle =20(5) -14$

STEP 12

implify the equation to find the measure of $\angle2$ .
$m \angle2 =100 -14$

STEP 13

Calculate the final value of $m \angle2$ .
$m \angle2 =86$ The measure of $\angle2$ is86 degrees.

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