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

Studdy Solution

STEP 1

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

STEP 2

Vertical angles are equal in measure. So, we can set the measures of $\angle1$ and $\angle2$ equal to each other.
$m \angle1 = m \angle2$

STEP 3

Substitute the given expressions for the measures of $\angle1$ and $\angle2$ into the equation.
$17x +1 =20x -14$

STEP 4

To solve for $x$ , we first need to isolate $x$ terms on one side of the equation. 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, we isolate $x$ by adding $14$ to both sides of the equation.
$1 +14 =3x -14 +14$

STEP 7

implify the equation.
$15 =3x$

STEP 8

Finally, we solve for $x$ by dividing both sides of the equation by $3$ .
$x = \frac{15}{3}$

STEP 9

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

STEP 10

Now that we have the value of $x$ , we can find the measure of the angles by substituting $x =5$ into the expressions for $m \angle$ and $m \angle2$ .
$m \angle =17x +$ $m \angle2 =20x -14$

STEP 11

Substitute $x =5$ into the expressions for $m \angle$ and $m \angle$ .
$m \angle =17(5) +$ $m \angle =20(5) -14$

STEP 12

Calculate the measures of $\angle$ and $\angle2$ .
$m \angle =85 + =86$ $m \angle2 =100 -14 =86$ The measure of $\angle$ and $\angle2$ is $86$ degrees.

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