trapezium ABCD, with AB and DC being parallel, with diagonal connecting A and C, angle ABC is 86, angle ADC is y, angle dac is 66 and angle bac is x,

Question

trapezium ABCD, with AB and DC being parallel, with diagonal connecting A and C, angle ABC is 86, angle ADC is y, angle dac is 66 and angle bac is x,

no angle given for bcd or bca or acd.

find x and y,

So I said that BCD is 94 deg, but then I get stuck

I think I'm probably missing some rule or something but not sure what it is.

Answer 1

I agree that bcd is 94°

similarly, angle acd is x, so x+y+66=180.

Still looking for another angle (as it were) to connect x and y.

Answer 2

I think it might be an error in the question, but thanks for trying at least I know it's not just me.

Answer 3

To find the values of x and y in trapezium ABCD, we can use a few geometric properties and rules. Let's go step by step:

1. First, let's examine the angles in triangle BAC. We are given that angle BAC = x and angle BCA = 86 degrees. Since the sum of the angles in any triangle is 180 degrees, we can find angle ABC as follows:

Angle ABC = 180 - (angle BAC + angle BCA)
= 180 - (x + 86)
= 94 - x

2. Next, let's consider triangle DAC. We are given that angle DAC = 66 degrees. Again, using the fact that the sum of the angles in a triangle is 180 degrees, we can find angle ADC:

Angle ADC = 180 - (angle DAC + angle ACD)
= 180 - (66 + y)
= 114 - y

3. Now, since AB is parallel to DC, angle ABC is supplementary to angle BCD. Therefore, angle BCD = 180 - angle ABC = 180 - (94 - x) = 86 + x.

4. Similarly, angle ADC is supplementary to angle DAC. Therefore, angle ACD = 180 - angle ADC = 180 - (114 - y) = 66 + y.

Now, we have the values of angle BCD (86 + x) and angle ACD (66 + y). However, without further information or constraints, we cannot determine the exact values of x and y. The problem is underdetermined, meaning multiple values for x and y can satisfy the given conditions.