Question

Solve for x. Find the angle measures. Angle AOB=x+3, angle AOC=2x+11, angle BOC=4x-7

Answer 1

x=5

`\angle AOC=21`

`\angle AOB=8`

`\angle BOC=13`

Explanation:

We are given that

`\angle AOB=x+3`

`\angle AOC=2x+11`

`\angle BOC=4x-7`

We have to solve for x and find the angle measures

`\angle AOC=\angle AOB+\angle BOC`

`2x+11=x+3+4x-7`

`2x+11=5x-4`

`11+4=5x-2x`

`15=3x`

`x=(15)/(3)=5`

Substitute the value of x then, we get

`\angle AOC=2(5)+11=21`

`\angle AOB=5+3=8`

`\angle BOC=4(5)-7=13`

Answer 2

x=5

AOB = 8

BOC = 13

AOC = 21

Explanation:

Angle AOB and Angle BOC is equal to Angle AOC.

AOB = x+3

BOC = 4x-7

AOC= 2x+11

AOB + BOC = AOC

x+3+4x-7 = 2x+11

5x-4 = 2x+11

3x = 15

x = 5

Therefore, the value of x is 5.

Angle AOB = x+3

AOB = 5+3

AOB = 8

Angle BOC = 4x-7

BOC = 4(5)-7

BOC = 13

Angle AOC = 2x+11

AOC = 2(5)+11

AOC = 21

!!