ABCD is a rhombus with one angle BAD = 50 degree, find angles x & y
I have no idea what your x and y stand for, but in a rhombus, opposite angles are equal and adjacent angles add up to 180°
So the other angle is 130°
x 25 and y 25
To find angles x and y in the rhombus ABCD with one angle BAD = 50 degrees, we can use the properties of rhombuses.
1. First, we know that opposite angles in a rhombus are equal. Since angle BAD is 50 degrees, angle ABD is also 50 degrees.
2. We can use the fact that the sum of angles in a triangle is 180 degrees to find the other angles.
3. In triangle ABD, the sum of angles ABD, ADB, and BAD is equal to 180 degrees.
- Angle ABD = 50 degrees (given)
- Angle ADB = y degrees (to be found)
- Angle BAD = 50 degrees (given)
Therefore, 50 + y + 50 = 180 degrees.
4. Simplifying the equation, we have:
100 + y = 180
5. Subtracting 100 from both sides, we have:
y = 180 - 100
y = 80 degrees
So, angle y in rhombus ABCD is 80 degrees.
6. Since opposite angles in a rhombus are equal, angle CBA is also 50 degrees.
7. We can use the fact that the sum of angles in a triangle is 180 degrees to find the other angles.
8. In triangle ABC, the sum of angles ABC, BAC, and CBA is equal to 180 degrees.
- Angle ABC = x degrees (to be found)
- Angle BAC = 180 - 50 - 50 (sum of angles in triangle ABD)
- Angle CBA = 50 degrees (given)
Therefore, x + (180 - 50 - 50) + 50 = 180 degrees.
9. Simplifying the equation, we have:
x + 80 = 180
10. Subtracting 80 from both sides, we have:
x = 180 - 80
x = 100 degrees
So, the angles x and y in rhombus ABCD are 100 degrees and 80 degrees, respectively.
To find angles x and y in the given rhombus ABCD, we need to use the properties of a rhombus.
In a rhombus, opposite angles are equal. So, angle BCD is also 50 degrees.
Let's label the angles of the rhombus as shown below:
A
/ \
/ \
D-----C
\ /
\ /
B
Now, we can solve for angles x and y:
Angle ABD = (180 - angle BAD)/2 (Since the sum of angles in a triangle is 180 degrees)
Angle ABD = (180 - 50) / 2 = 130/2 = 65 degrees
In a rhombus, opposite angles are equal. So, angle ABC also measures 65 degrees.
Since angle ABC is opposite to angle BCD, they are equal. So, angle BCD is also 65 degrees.
Now, to find angle ACD, we can subtract angle BCD from 180:
Angle ACD = 180 - angle BCD = 180 - 65 = 115 degrees
Finally, to find angle ADB (which is equivalent to angle ADC), we can subtract angle ABD from 180:
Angle ADB = 180 - angle ABD = 180 - 65 = 115 degrees
Therefore, angles x = angle ADB = angle ADC = 115 degrees, and angles y = angle ABC = angle BCD = 65 degrees.