isosceles triangle

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zia
Posts: 5
Joined: Sat Jan 09, 2016 11:32 am

isosceles triangle

Post by zia »

can anyone help to solve this problem?
In an isosceles triangle, twice one of the angles is 5 times as big as another. What is not a possible size for one of the angles?
The options are 100, 75,40,30,20
yoyo123
Posts: 8099
Joined: Mon Jun 18, 2007 3:32 pm
Location: East Kent

Re: isosceles triangle

Post by yoyo123 »

In an isosceles triangle 2 of the angles are the same.
You can use this fact and trial and error.

Also you cannot exceed the maximum number of degrees in a triangle.
doodles
Posts: 8300
Joined: Tue Oct 27, 2009 9:19 pm

Re: isosceles triangle

Post by doodles »

Here the answer is 20 apparently :D
target2016
Posts: 60
Joined: Sun Oct 19, 2014 12:52 pm

Re: isosceles triangle

Post by target2016 »

and using algebra...

If,

x = the size of one of the equal pair of angles.
y = the third angle.

We have two sets of equations (possibilities):

2x = 5y
2x + y = 180
OR
2y = 5x
2x + y = 180


Solving first pair, we get
x = 75
y = 30

Solving second pair, we get
x = 100
y = 40

Hence, the remaining i.e 20, must be the answer.
Guest55
Posts: 16254
Joined: Mon Feb 12, 2007 2:21 pm

Re: isosceles triangle

Post by Guest55 »

target 2016 - Algebra makes this harder and is not appropriate for this question.

SImple trial and improvement gets the answer in a few seconds.
target2016
Posts: 60
Joined: Sun Oct 19, 2014 12:52 pm

Re: isosceles triangle

Post by target2016 »

It's a matter of choice. There is no one way, but this way makes it show how we arrived at the answer better. Personally I don't like "trial and error"... takes me ages!
Guest55
Posts: 16254
Joined: Mon Feb 12, 2007 2:21 pm

Re: isosceles triangle

Post by Guest55 »

As mathematicians we judge the best method as the shortest and most elegant - the choice of x and y also makes it harder to remember which variable is which. Note I said trial and improvement - not error!

e = equal angle would have been a better choice.
target2016
Posts: 60
Joined: Sun Oct 19, 2014 12:52 pm

Re: isosceles triangle

Post by target2016 »

Now that's getting pedantic. Like I said - it's a matter of choice :D
yoyo123
Posts: 8099
Joined: Mon Jun 18, 2007 3:32 pm
Location: East Kent

Re: isosceles triangle

Post by yoyo123 »

I would expect most children in y5/6 to solve it without algebra.

Agree trial and improvement, rather than error :oops:
target2016
Posts: 60
Joined: Sun Oct 19, 2014 12:52 pm

Re: isosceles triangle

Post by target2016 »

try again! :wink:
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