Find missing angles In pentagon ABCDE and angle ABC=angle BCD=CDE

[richiesmasher]

Hello, here is a pentagon ABCDE and angle ABC=angle BCD=CDE

Calculate giving a reason for each answer the magnitudes of angles (i) ABC and (ii) CDX.

Here is my attempt, for angle ABC, I know the angles in a pentagon add up to 540 degrees, and I know it can be consisting of three separate triangles.

Since the three angles listed are equal, then clearly the line AD which makes the first triangle AED, bisects angle CDE which clearly means each bisector forming a triangle will give you half of the angle bisected.

So I thought, if I draw a line from B to D, the triangle BDC that would be formed would be all equal angles as all the angles would be bisected, so by that logic angle ABC would be 180/3 = 60.

If there is any other obvious method I'm missing out please tell me any angle rules etc.

AS for angle CDX I'm a bit unsure.

 

[lev888]

The 3 angles marked by X are not the same 3 angles described as equal in the post. Please clarify.

 

[richiesmasher]

The 3 angles marked by X are not the same 3 angles described as equal in the post. Please clarify.

Sorry I meant angle ABC as the first one, typo.

 

[Dr.Peterson]

Hello, here is a pentagon ABCDE and angle ABC=angle BCD=CDE

Calculate giving a reason for each answer the magnitudes of angles (i) ABC and (ii) CDX.

Here is my attempt, for angle ABC, I know the angles in a pentagon add up to 540 degrees, and I know it can be consisting of three separate triangles.

Since the three angles listed are equal, then clearly the line AD which makes the first triangle AED, bisects angle CDE which clearly means each bisector forming a triangle will give you half of the angle bisected.

So I thought, if I draw a line from B to D, the triangle BDC that would be formed would be all equal angles as all the angles would be bisected, so by that logic angle ABC would be 180/3 = 60.

View attachment 9110
If there is any other obvious method I'm missing out please tell me any angle rules etc.

AS for angle CDX I'm a bit unsure.

Did you give us all the information in the problem? I don't see how you can conclude that AD bisects angle CDE, and so on. And triangle BCD can't possibly be equilateral, since angle DBC is less than angle ABC, which is equal to angle BCD.

Also, in the picture it looks as if angles BAE and AED are right angles; is that something you are told? I think you need more information than you have given.

 

[richiesmasher]

Did you give us all the information in the problem? I don't see how you can conclude that AD bisects angle CDE, and so on. And triangle BCD can't possibly be equilateral, since angle DBC is less than angle ABC, which is equal to angle BCD.

Also, in the picture it looks as if angles BAE and AED are right angles; is that something you are told? I think you need more information than you have given.

No that really is all the information given, there is part 2 stating
''Given that AD = 18cm and angle EAD = 30 degrees, calculate the length of (i)DE (ii)AE''

But for the first part thats all that is given, that picture, and the information that all three angles marked X inside the pentagon are equal.

 

[richiesmasher]

Any ideas anyone?

 

[mmm4444bot]

So far, the ideas are that you don't have enough information and the diagram needs clarification. (DrPeterson asked whether you were told some angles are 90 degrees.) Also, they should not have used the same symbol to represent both a point and an angle measurement.

Can you attach an image of what you were given?

 

[richiesmasher]

Hey

 

[mmm4444bot]

ABCDE is a concave irregular pentagon, so any interior angle or side length can vary from its counterparts.

If you would like to assume that angles BAE and DEA are 90°, then you can find $\displaystyle x$ because you know that the sum of interior angles is 540°.

 

[Dr.Peterson]

Hey
View attachment 9116

It is a poorly written problem, but we must be expected to assume that angles BAE and AED are right angles, and EDX is a line, as they appear, since otherwise we can't solve it. This makes the questions easy. Can you solve it with those assumptions?

 

[richiesmasher]

It is a poorly written problem, but we must be expected to assume that angles BAE and AED are right angles, and EDX is a line, as they appear, since otherwise we can't solve it. This makes the questions easy. Can you solve it with those assumptions?

Yes, I have solved the problem, I should have seen those shapes from the start.