in the following diagram AB||CD. find x,y,z
Answers
Answer:
angle q=angle y ( alternate interior angles)
y=40
angle x +angle y = 180 (linear pair)
x=140
angle r= angle z=50
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The value of x is 40°
The value of x is 40° The value of y is 90°
The value of x is 40° The value of y is 90° The value of z is 50°
GIVEN
AB || CD
TO FIND
The value of x, y and z
SOLUTION
We can simply solve the above problem as follows;
It is given that
AB || CD
Therefore,
∠PQR = ∠QPA (Alternate interior angles of traversal are equal)
Therefore,
∠QPA = x = 40° (i)
PQR is a triangle.
∠RPQ + ∠PQR + ∠QRP = 180° (Sum of interior angle of a triangle)
Therefore,
40 + 50 + y = 180
90 + y = 180
y = 180-90
y = 90°
Now,
∠x + ∠y + ∠z = 180° (Angle of straight line)
Putting the value of x, and y.
40 + 90 + z = 180
130 + z = 180
z = 180-130 = 50°
Hence,
- Hence, The value of x is 40°
- Hence, The value of x is 40° The value of y is 90°
- Hence, The value of x is 40° The value of y is 90° The value of z is 50°
Hence, The value of x is 40° The value of y is 90° The value of z is 50° #Spj2