Angle properties: Angles centered at a point?

[Frank212]

Homework Statement

Find what x is

I don't understand what to do with (3x-23).

Homework Equations

Angles centered at a point: a+b+c+d=360

https://drtayeb.files.wordpress.com/2011/03/igcse-math-extended.pdf
(here is a pdf of the textbook, Exercise 4A, 3i.)[/B]

The Attempt at a Solution

a+b+c+d=360
45+44=89
360-89=271
two angles left to solve for final equation: 3x,x and (3x-23)
(3x-23)? <- please tell me what to do with this, do you isolate it?

 

[Nidum]

Clue : Sum the whole lot into an equation for x :

3x + (3x - 23) + ------- = ??

 

[ehild]

Homework Statement

Find what x is
View attachment 104457
I don't understand what to do with (3x-23).

Homework Equations

Angles centered at a point: a+b+c+d=360

https://drtayeb.files.wordpress.com/2011/03/igcse-math-extended.pdf
(here is a pdf of the textbook, Exercise 4A, 3i.)[/B]

The Attempt at a Solution

a+b+c+d=360
45+44=89
360-89=271
two angles left to solve for final equation: 3x,x and (3x-23)
(3x-23)? <- please tell me what to do with this, do you isolate it?

There are four angles, a=45, b= x+44, c=3x-23, d=3x. They are expressed in terms of x. Just add the angles, 45 + (x+44) + (3x-23) + (3x) = 360. You get the equation for the unknown x. Collect the like terms and solve for x.

 

[Frank212]

There are four angles, a=45, b= x+44, c=3x-23, d=3x. They are expressed in terms of x. Just add the angles, 45 + (x+44) + (3x-23) + (3x) = 360. You get the equation for the unknown x. Collect the like terms and solve for x.

Thank you ehild, your explanation really helped a lot.

45+(x+44)+(3x-23)+3x=360
7x+66=360
7x=294
7x/7=294/7
x=42

 

[ehild]

Nice work!

Thank you ehild, your explanation really helped a lot.

45+(x+44)+(3x-23)+3x=360
7x+66=360
7x=294
7x/7=294/7
x=42