Question

What are the steps to this? Geometry is really hard and I don’t know how to get the answers. Please give me a step-by-step so I can learn!

Answer 1

`\sf x=8`

`\sf \angle AOB =30`

`\sf \angle BOC=50`

Explanation:

Given:

`\sf m\angle AOB=4x-2`

`\sf m\angle BOC=5x+10`

`\sf m\angle COD=2x+14`

To find:

x = ?

`\sf \angle AOB = ?`

`\sf \angle BOC= ?`

Solution:

According to the given symbol in the picture, we can say that:

`\sf \angle AOB =\angle COD`

Substitute the value:

`\sf 4x-2= 2x +14`

Subtract 2x and add 2 on both sides:

`\sf 4x-2-2x+2= 2x +14-2x+2`

`\sf 2x =16`

Divide by 2 on both sides:

`\sf x =(16)/(2)`

`\sf x=8`

Now

`\sf \angle AOB = 4x-2=4* 8 -2 = 32-2 =30`

`\sf \angle BOC=5x+10=5* 8 +10= 40+10=50`