Question

consider the following parallelogram and find the value of x, y, z​

Answer 1

Answer:

x = 50 degrees

y = 60 degrees

z = 40 degrees

Step-by-step explanation:

in parallelogram opposite sides are parallel.

So alternate interior angles will be equal

and sum of 2 adjacent angles of a parallelogram is always 180 degrees

so the angle adjacent to y = x (alternate interior angle)

so x + y = 180 - (40 + 30) = 110 degrees

angle vertically opposite to 100 degrees = 100 degrees (vertically opposite angles are equal)

in a Δ, sum of angles is 180 degrees.

so in the bottom most triangle, angles are x, 100 degrees, 30 degrees

so x + 100 + 30 = 180 degrees

so x = 180 - 130 = 50 degrees

as shown above, x + y = 110 degrees

so y = 110 - x = 110 - 50 = 60 degrees

In the right most triangle, angle adjacent to 100 degrees is 80 degrees (the 2 angles form a linear pair)

so the angles in the triangle are 80 degrees, 60 degrees, z

so 80 + 60 + z = 180 degrees

so z = 180 - (80 + 60)

so z = 40 degrees

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