# Quadrilateral angles and ratio

Discussion in 'Mathematics' started by MasterMaths, Apr 2, 2012.

1. ### MasterMaths

Sorry guys ... I feel really stupid posting this ... but am I going mad!?!? I'm preparing some revision materials for a session tomorrow, and have come across this question:
Angles in a quadrilateral are in the ratio 1:2:4:5.If the largest angle is 72&ordm;<font face="Calibri">, find the </font>value of the other three angles.
It then has a "wrong" solution which the pupil has to comment on, and then provide a correct solution themselves.
The "wrong" solution basically goes through 1+2+4+5 = 12. 360/12 = 30 so the other angles are 1x30=30, 2x30=60 and 4x30=120.

It seems to me that the question MUST BE WRONG!! How can the largest angle in a quadrilateral be 72? If the original question made no mention of 72 then the "wrong" solution would surely be totally correct!!
Please confirm that I haven't gone mad and I didn't leave my brain in the classroom when we broke up on Friday.

2. ### MasterMaths

Sorry guys ... I feel really stupid posting this ... but am I going mad!?!? I'm preparing some revision materials for a session tomorrow, and have come across this question:
Angles in a quadrilateral are in the ratio 1:2:4:5.If the largest angle is 72&ordm;<font face="Calibri">, find the </font>value of the other three angles.
It then has a "wrong" solution which the pupil has to comment on, and then provide a correct solution themselves.
The "wrong" solution basically goes through 1+2+4+5 = 12. 360/12 = 30 so the other angles are 1x30=30, 2x30=60 and 4x30=120.

It seems to me that the question MUST BE WRONG!! How can the largest angle in a quadrilateral be 72? If the original question made no mention of 72 then the "wrong" solution would surely be totally correct!!
Please confirm that I haven't gone mad and I didn't leave my brain in the classroom when we broke up on Friday.

3. ### PaulDGOccasional commenter

As there are 360 degrees in a quadrilateral, it's simply not possible for the largest to be 72 degrees. (4x72 < 360) Something's missing from the question, as you say.

4. ### MasterMaths

Not only is something missing, it just seems so fundamentally wrong! I can't see what the person who was writing it was trying to achieve. It's part of a series of otherwise good questions in which the pupil corrects some common mistakes ... but I just can't see what the mistake s/he was trying to highlight was. Oh well - at least I'm not going mad!

5. ### KarvolOccasional commenter

Perhaps - with tongue slightly in cheek - with reference to the debacle of the decision (?) maths paper last year, he or she is trying to point out that sometimes examiners get it wrong?
Either that or it is a genuine error.

6. ### KarvolOccasional commenter

Reading the question again, it appears to be a question using pentagons ( perhaps with the 72 degrees ) being transposed to quadrilaterals without the numbers being properly checked.
Clearly if you change the original angle, then the question starts to make sense.
is obviously wrong as it doesn't take into account the original condition about the given angle being the largest.
So my interpretation is that it is a simple error on behalf of the author.