Question

in each case find the value of x and y

Answer 1

(1) diagonals of rectangle bisect each other. (2)
OA=OB
Now by Theron angles opposite to equal side are equal. (3)
Angle OAB=angle OBA=35°
Now in triangle OAB
angle OAB+angle OBA+angle AOB=180°
Therefore angle AOB=110°
angle AOB=y°=110°
Now 35°+x°=90. Angle of rectangle
x°=55°
(2)angle AOB +angle BOC=180° (linear pair)
Angle BOC=70°
Now by therom stated in(2)&(3)
Angle OBC=x°
Now
Angle OBC+ angle BOC +x°=180°.
(Angle sum property of triangle)
2x°=110°
x°=55°
Now x°+y°=90°. Angle of rectangle
Y°=90°-55°
Y°=35°

Answer 2

hi friend

here's your answer looking for

1).
in triangle AOB
angle OAB= angle OBA ( opposite angle of iso triangle)

angle OBA =35 degree

and,
angle ABC =90 degree. ( angle of rectangle)

so,
angle OBA +x =90

30+x=90

x= 55


and, in triangle AOB

angle OAB+ angle OBA + angle AOB = 180.

35+ 35 + angle AOB = 180. ( angle OAB = angle OBA)

angle AOB= 110

angle AOB = y = 110 ( vertically opposite angle)

2).


angle AOB =angle DOC. ( vertically opposite angle )

angle DOC = 110

in triangle DOC,

Angle ODC = y ( opposite angle of iso triangle )

angle ODC +y+ angle DOC = 180

y + y + 110 = 180.

y= 35

and,

x+y = 90. ( each angle of rectangle)

x = 90-35

x= 55

hope it's helpful to you

From brainly star Amaytripathi19