ABCD is a square. The measure of angle 4 = 3x - 3. Find x.

Square ABCD, diagonals bisect at E. Angle ADE is angle 4

ABCD is a square. The measure of angle 4 = 3x - 3. Find x.

Square ABCD, diagonals bisect at E. Angle ADE is angle 4

16

47

29

45

1 answer

To find x, we need to set up an equation using the information given:

Angle 4 = 3x - 3

Since angle 4 and angle ADE are the same (as per the information given), we can say that:

3x - 3 = ADE

Since E is the midpoint of diagonal AC, angles ADE and CDE are congruent.

Therefore, ADE = CDE

Which means:

3x - 3 = CDE

Since angle CDE is a right angle in a square, it's equal to 90 degrees.

Therefore:

3x - 3 = 90

Now, we solve for x:

3x - 3 = 90
3x = 93
x = 31

Therefore, x = 31

Final Answer: 31.