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!

Question

asked Feb 4, 2024 218k views

1 Answer

Wodesuck · Answer 1 · 2024-02-11T04:38:32+0000

Answer:

$\sf x=8$

$\sf \angle AOB =30$

$\sf \angle BOC=50$

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

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

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