Question

then, solve for the missing angles
28.

m∠1 =

m∠2 =

m∠3 =

m∠4 =

29.

m∠1 =

m∠2 =

m∠3 =

m∠4 =

30.

m∠1 =

m∠2 =

m∠3 =

then, solve for x and find the m∠1.
31.

x =

m∠1 =

32.

x =

m∠1 =

Explanation:

Step1: Solve Problem 18

Step1a: Find $m\angle1$

$\angle1$ and $55^\circ$ are supplementary.
$m\angle1 = 180^\circ - 55^\circ = 125^\circ$

Step1b: Find $m\angle2$

$\angle2$ and $30^\circ$ are vertical angles.
$m\angle2 = 30^\circ$

Step1c: Find $m\angle3$

$\angle3$ and $\angle1$ are vertical angles.
$m\angle3 = 125^\circ$

Step1d: Find $m\angle4$

$\angle4$ and $55^\circ$ are vertical angles.
$m\angle4 = 55^\circ$

Step2: Solve Problem 19

Step2a: Find $m\angle1$

$\angle1$ and $42^\circ$ are vertical angles.
$m\angle1 = 42^\circ$

Step2b: Find $m\angle2$

$\angle2$ and $42^\circ$ are complementary.
$m\angle2 = 90^\circ - 42^\circ = 48^\circ$

Step2c: Find $m\angle3$

$\angle3$ is a right angle.
$m\angle3 = 90^\circ$

Step2d: Find $m\angle4$

$\angle4$ and $\angle2$ are vertical angles.
$m\angle4 = 48^\circ$

Step3: Solve Problem 20

Step3a: Find $m\angle1$

$\angle1$ and $37^\circ$ are complementary.
$m\angle1 = 90^\circ - 37^\circ = 53^\circ$

Step3b: Find $m\angle2$

$\angle2$ and $37^\circ$ are vertical angles.
$m\angle2 = 37^\circ$

Step3c: Find $m\angle3$

$\angle3$ and $\angle1$ are supplementary.
$m\angle3 = 180^\circ - 53^\circ = 127^\circ$

Step4: Solve Problem 21

Step4a: Solve for $x$

Vertical angles are equal: $4x-18 = 2x+32$
$4x-2x = 32+18$
$2x = 50$
$x = 25$

Step4b: Find $m\angle1$

$\angle1$ is supplementary to $2x+32$.
$2(25)+32 = 82^\circ$
$m\angle1 = 180^\circ - 82^\circ = 98^\circ$

Step5: Solve Problem 22

Step5a: Solve for $x$

Vertical angles are equal: $20x+12 = 25x-18$
$12+18 = 25x-20x$
$30 = 5x$
$x = 6$

Step5b: Find $m\angle1$

$\angle1$ is supplementary to $20x+12$.
$20(6)+12 = 132^\circ$
$m\angle1 = 180^\circ - 132^\circ = 48^\circ$

Answer:

Problem 18

$m\angle1 = 125^\circ$
$m\angle2 = 30^\circ$
$m\angle3 = 125^\circ$
$m\angle4 = 55^\circ$

Problem 19

$m\angle1 = 42^\circ$
$m\angle2 = 48^\circ$
$m\angle3 = 90^\circ$
$m\angle4 = 48^\circ$

Problem 20

$m\angle1 = 53^\circ$
$m\angle2 = 37^\circ$
$m\angle3 = 127^\circ$

Problem 21

$x = 25$
$m\angle1 = 98^\circ$

Problem 22

$x = 6$
$m\angle1 = 48^\circ$