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simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Can't wrap my dumb head around this angles problem

An angle "p" exists that is complementary to angle g on one side. On the other side, the angle p is supplementary to angle h. The sum of the three angles is 200°. What is the measure of this common angle p? (Show your work AND upload a drawing of this problem.)

So, p + g = 90
p + h = 180
p + g + h = 200?
Where in the world do I start with this? And the drawing? Aggghhh. I'm really not good with angles.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Can't wrap my dumb head around this angles problem

Hi, Your three equations are correct, so this ceases to be an angles question and becomes an algebraic one.
Add together the first two (2p + g + h) and subtract the third to get p.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycmathguy

Member

Registered: 2021-06-02

Posts: 53

Re: Can't wrap my dumb head around this angles problem

Hi, Your three equations are correct, so this ceases to be an angles question and becomes an algebraic one.
Add together the first two (2p + g + h) and subtract the third to get p.

Bob

Is this not three equations in 3 unknowns?

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Can't wrap my dumb head around this angles problem

Hi, Your three equations are correct, so this ceases to be an angles question and becomes an algebraic one.
Add together the first two (2p + g + h) and subtract the third to get p.

Bob

Hello, thanks for replying. I just can't wrap my head around that. What am I supposed to do?? (＠_＠)

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Can't wrap my dumb head around this angles problem

Nevermind, I think I've got it. P = 70?
You can do p + (90 - p) + (180 - p) = 200, remove the brackets, combine the "p"s, multiply negatives in, which leaves me with p = -200 + 90 + 18. So, that means p = 70?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Can't wrap my dumb head around this angles problem

hi simonmagusflies

p = 70 is what I got too.

Your algebra is excellent and probably simpler than mine.  Just for the record here's what I did:

p+g = 90
p+h = 180

so 2p + g + h = 270

we are told P + g + h = 200 so subtracting one equation from the other gives

p = 70

But my first approach was to make a diagram.

I started by drawing a right angle, ACD

Then I split this into angle g and angle p by marking the line BC.

I extended AC to E so that ACE is a straight line and angle ACE = 180.

I extended BC to F so that BCF is a straight line and angle BCF = 180.

I marked on angle h = DCF

angle ECF = angle ACB = g (vertically opposite angles)

Reflex angle ACF is given as 200 and angle  ACE = 180 therefore g = 20.

So p = 70

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob