Diagonals of a parallelogram WXYZ intersect each other at point O. If ∠XYZ=135° then what is the measure of ∠XWZ and ∠YZW ? If L(OY)= 5 cm then L(WY)= ?
Answers
Answer:
∠XWZ = 135°
∠YZW = 45°
WY = 10 cm
Step-by-step explanation:
In a parallelogram opposite angles are Equal
and sum of adjacent angle = 180°
∠XYZ=135°
∠XWZ is opposite to ∠XYZ
=> ∠XWZ = ∠XYZ = 135°
=> ∠XWZ = 135°
∠YZW is adjacent to ∠XYZ
=> ∠YZW + ∠XYZ = 180°
=> ∠YZW + 135° = 180°
=> ∠YZW = 45°
Diagonals of a parallelogram bisect each other
hence OY = OW
WY = OY + OW
WY = OY + OY
WY = 2 * OY
WY = 2 * 5
WY = 10 cm
Step-by-step explanation:
WXYZ is a parallelogram.
XYZ = XWZ.......( the opposite angle of a parallelogram
are congruent )
But, XYZ = 135°
i.e. XWZ = 135°
XYZ + YZW = 180°...........( Interior angle )
135° + YZW = 180°
YZW = 180° - 135°
YZW = 45°
Also,
OY = ½ × WY..........( the diagonal of a parallelogram
bisect each other )
5 = ½ × WY
5 × 2 = WY
WY = 10 cm.