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