Math Is Fun Forum

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Geometry Angle Problem

I am stuck on this problem:

When the measures of the angles of a triangle are placed in order, the difference between the middle angle and smallest angle is equal to the difference between the middle angle and largest angle. If one of the angles of the triangle has measure 23 degrees, then what is the measure in degrees of the largest angle of the triangle?

Thanks for the help

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Angle Problem

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry Angle Problem

Hi denis_gylaev,

x = smallest, y = middle, z = largest, and y - x = z - y.

Now we can write the following equations:
1. 2y = x + z
2. x + y + z = 180 (ie, the sum of the angles in a triangle).

z cannot = 23: z is the largest, and so, from equation #2, x + y + z = less than 69 (ie, less than the required 180).
y cannot = 23: if y = 23, then, from equation #1, x + z = 46, which, when added to y, totals 69 (ie, less than the 180 required by equation #2).

That leaves x = 23.

From equation #1 we get:
2y = 23 + z
y = (23 + z) / 2

Substitute for y in equation #2:
23 + (23 + z) / 2 + z = 180

And you should be able to finish off from there.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Geometry Angle Problem

Wow. What a fine question, denis_gylaev.

Dear bobbym and phrontister, I am in tune with your solutions. I totally agree and I'm actually getting that too.
Hi anyway. I've been away for a while.

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Only a friend tells you your face is dirty.