Question

For questions 13-15, find X so that 9 ||
13. X=
14. X=
15. X=
PLEASEE

Answer 1

`13.)x=7\\\\14.)x=12\\\\15.)x=23`

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:

`15x+3=108\\\\15x+3-3=108-3\\\\15x=105\\\\(15x)/(15)=(105)/(15)\\\\x=7`

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:

`(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\\\\(18x)/(18)=(216)/(18)\\\\ x=12`

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:

`90+2x`

Now set this value equal to the other angle and solve for x:

`90+2x=5x+21\\\\90-21+2x=5x+21-21\\\\69+2x=5x\\\\69+x-2x=5x-2x\\\\69=3x\\\\(69)/(3)=(3x)/(3) \\\\ x=23`

:Done