Question

I need help please. It will really help me

Answer 1

x = 15

∠AOB = 15°

∠BOC = 165°

Explanation:

Angles on a straight line add up to 180°

`\sf \implies \angle AOB + \angle BOC=180`

Substitute the given expressions for the angles:

`\sf \implies (2x - 15) + 11x = 180`

Collect and combine like terms:

`\sf \implies 2x +11x- 15=180`

`\sf \implies 13x- 15=180`

Add 15 to both sides:

`\sf \implies 13x- 15+15=180+15`

`\sf \implies 13x=195`

Divide both sides by 13:

`\sf \implies (13x)/(13)=(195)/(13)`

`\sf \implies x=15`

Now substitute the found value of x into the expressions for each angle:

`\sf \implies \angle AOB =2(15)-15=15^(\circ)`

`\sf \implies \angle BOC =11(15)=165^(\circ)`