Question

In the given figure, If ABCD is a square, then the value of x is:​

Answer 1

Answer:

Refer the attachment. x = 60 degree

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Answer 2

Answer:

Using the properties of, Vertically Opposite Angle, ABCD Square's corner right angle, and the angle sum of the triangle, we can solve the given question, to get x=60°

Step-by-step explanation:

Let the 105° intersecting point is, E.

So, the rough diagram:

D                     C

              E  

                       F

A                     B

The angle, DEC=105°

So, with the help of Vertically Opposite angle, of the Straight line degree=180*

So, angle CEF= 180°-105°=75°

Similarly, since it's already given that, it's a square, so, the diagonals cut the corner right angle equally into 45°  (∠ECF)

Finally, taking the CEF Triangle,

Since, the sum of angles in a Triangle=180°

So, x+∠CEF + ∠ECF=180°

     x+75°+45°=180°

     x=180°-(75°+45°)

     x=180°-120°

     x=60°

Important insights:

Vertical angles are formed by two intersecting lines, where each angle is opposite to another. Vertical angles are always equal in measure, which means that they have the same angle value. For example, if angle A is 30 degrees, then the vertical angle B must also be 30 degrees.

A square corner is also known as a right angle. It is formed when two lines or line segments meet at a 90-degree angle. A right angle is denoted by a small square in the vertex where the two lines meet. A right angle is an important concept in geometry, as it creates the basis of the Pythagorean theorem and other important geometric principles.

The sum of angles in a triangle is always 180 degrees. This is known as the triangle angle sum theorem. Regardless of the size or shape of the triangle, the sum of its three angles will always be 180 degrees. For example, if angle A is 60 degrees and angle B is 80 degrees, then the third angle C must be 40 degrees in order for the sum of all three angles to be 180 degrees. The triangle angle sum theorem is an essential concept in geometry, as it is used to solve for missing angles in various geometric shapes and applications.

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