Answer:
[tex]13.)x=7\\\\14.)x=12\\\\15.)x=23[/tex]
Step-by-step explanation:
13. The given angles are alternate interior angles, so these angles are congruent. Make an equation in which they are equal to each other and solve for x:
[tex]15x+3=108\\\\15x+3-3=108-3\\\\15x=105\\\\\frac{15x}{15}=\frac{105}{15}\\\\x=7[/tex]
14. The given angles are same-side interior angles, so they are supplementary. Make an equation in which the sum of the angles is equal to 180° and solve for x:
[tex](11x-28)+(7x-8)=180\\\\11x-28+7x-8=180\\\\11x+7x-28-8=180\\\\18x-36=180\\\\18x-36+36=180+36\\\\18x=216\\\\\frac{18x}{18}=\frac{216}{18}\\\\ x=12[/tex]
15. If you remove the horizontal line, the given angles are corresponding angles. These are congruent. However, make sure to add back the horizontal transversal line. Since this creates a 90°, add this to the given angle value:
[tex]90+2x[/tex]
Now set this value equal to the other angle and solve for x:
[tex]90+2x=5x+21\\\\90-21+2x=5x+21-21\\\\69+2x=5x\\\\69+x-2x=5x-2x\\\\69=3x\\\\\frac{69}{3}=\frac{3x}{3} \\\\ x=23[/tex]
:Done
