9. In the following figures, find the values of y and z.
x+50
x-50
5x+800
प्रिय
2x+100
Answers
ABCD is a rectangle. We know that the diagonals of the rectangle are equal and bisect each other.
⟹BD=AC and AO=BO=OC=OD
In △ABO,
∠OAB=∠OBA=50
∘
---Angles opposite to the equal sides in a triangle are equal.
In △AOB,
∠AOB+∠OAB+∠OBA=180
∘
---sum of interior angles of a triangle
∴∠AOB=x=180
∘
−50
∘
−50
∘
=80
∘
Solution (ii):
ABCD is a rectangle. We know that the diagonals of the rectangle are equal and bisect each other.
⟹BD=AC and AO=BO=OC=OD
∠OCD+∠DCE=180
∘
---Angles on a straight line
∠ODC=180
∘
−146
∘
=34
∘
In △DOC,
∠ODC=∠OCD=34
∘
---Angles opposite to the equal sides in a triangle are equal.
In △DOC,
∠CDO+∠DCO+∠DOC=180
∘
---sum of interior angles of a triangle
∴∠DOC=180
∘
−34
∘
−34
∘
=112
∘
∠DOC=∠AOB=x=112
∘
---Vertically Opposite angles
∠DCO=∠OAB=y=34
∘
---Alternate angles