Question

In the given figure is a parallelogram, find the values of x & y. ​

Answer 1

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Here's the detailed answer to your question.

Answer:

The value of x is 29 degrees, y is 73 degrees, and z is 102 degrees.

Previous Knowledge:

Parallelogram  -  Basic properties

• It is a quadrilateral where both pairs of opposite sides are parallel.
• Opposite sides are congruent (AB = DC).
• Opposite angles are congruent (D = B).
• Consecutive angles are supplementary (A + D = 180°).
• If one angle is right, then all angles are right.
• The diagonals of a parallelogram bisect each other.
• Each diagonal of a parallelogram separates it into two congruent triangles.
• Alternate interior angles of a parallelogram are equal.

Angle sum property of a triangle: The sum of all 3 angles of a triangle is always 180 degrees.

Step-by-step explanation:

We know, the alternate interior angles of a parallelogram are equal.

So, angle x = 29 degrees  --------------------------(1)

Also, by the angle sum property of triangle, we know the sum of all 3 angles adds up to 180 degrees.

That is, x + y + 78 =  180

=>       29 + y + 78 =  180

=>              y + 107 =  180

=>                         y = 180 - 107

=>                         y =  73 degrees-------------------------(2)

Also,

angle z = angles (x + y)  [ Exterior angle = Sum of interior opposite angles]  

=> z =  29 + 73  = 102 degrees              [From (1) and (2)]

Hence, the value of x is 29 degrees, y is 73 degrees, and z is 102 degrees.

Thanks!

Answer 2

Answer:

The value of x is 29 degrees, y is 73 degrees, and z is 102 degrees.

Previous Knowledge:

• It is a quadrilateral where both pairs of opposite sides are parallel.
• Opposite sides are congruent (AB = DC).
• Opposite angles are congruent (D = B).
• Consecutive angles are supplementary (A + D = 180°).
• If one angle is right, then all angles are right.The diagonals of a parallelogram bisect each other.
• Each diagonal of a parallelogram separates it into two congruent triangles.

• Alternate interior angles of a parallelogram are equal.
  Angle sum property of a triangle: The sum of all 3 angles of a triangle is always 180 degrees.

Step-by-step explanation:

We know, the alternate interior angles of a parallelogram are equal.

So, angle x = 29 degrees  --------------------------(1)

Also, by the angle sum property of triangle, we know the sum of all 3 angles adds up to 180 degrees.

That is, x + y + 78 =  180

=>       29 + y + 78 =  180

=>              y + 107 =  180

=>                         y = 180 - 107

=>                         y =  73 degrees-------------------------(2)

Also,

angle z = angles (x + y)  [ Exterior angle = Sum of interior opposite angles]  

=> z =  29 + 73  = 102 degrees              [From (1) and (2)]

Hence, the value of x is 29 degrees, y is 73 degrees, and z is 102