Question

What are the answers to this please. thank you. ​

Answer 1

8. x = 9

9. x = 9

10. x = 36

11. x = 8

Explanation:

Question 8

As the base of the triangle has been bisected, set the expressions either side of the perpendicular bisector equal to each other and solve for x:

`\implies 5x-15=2x+12`

`\implies 5x-15-2x=2x+12-2x`

`\implies 3x-15=12`

`\implies 3x-15+15=12+15`

`\implies 3x=27`

`\implies (3x)/(3)=(27)/(3)`

`\implies x=9`

Question 9

As the base of the triangle has been bisected, set the expressions either side of the perpendicular bisector equal to each other and solve for x:

`\implies 8x-63=4x-27`

`\implies 8x-63-4x=4x-27-4x`

`\implies 4x-63=-27`

`\implies 4x-63+63=-27+63`

`\implies 4x=36`

`\implies (4x)/(4)=(36)/(4)`

`\implies x=9`

Question 10

Angles on a straight line sum to 180°. Therefore, as the other angle on the line is a right angle, equate the given expression to 90° and solve for x:

`\implies (3x-18)^(\circ)=90^(\circ)`

`\implies 3x-18=90`

`\implies 3x-18+18=90+18`

`\implies 3x=108`

`\implies (3x)/(3)=(108)/(3)`

`\implies x=36`

Question 11

Interior angles of a triangle sum to 180°. Therefore, equate the sum of the given angles to 180° and solve for x:

`\implies 90^(\circ)+(3x)^(\circ)+(8x+2)^(\circ)=180^(\circ)`

`\implies 90+3x+8x+2=180`

`\implies 11x+92=180`

`\implies 11x+92-92=180-92`

`\implies 11x=88`

`\implies (11x)/(11)=(88)/(11)`

`\implies x=8`