Question

In the given figure, AB parallel to CD and angle AOC = x. If angle OAB=104 and angle OCD=116, Find the value of x​

Answer 1

Answer:

<Aoc =x°

first draw line passing with O

and then ,now

<OAB = 104°

the by (consecutive )

180 = <OAB + <1

<1 = (180 - 104 )

<1=. 76°

now second step ,

<OCD = 116°

then ,180 = <OCD + <2

<2= (180 - 116 )

<2= 64°

= Now add <1 + <2

= (76+ 64)°

x° = 140°

Answer 2

Answer:

x = 140°

Step-by-step explanation:

If you extend lines AO and DC, they will intersect at a point, say X (draw the new figure to get a better understanding of the later part)

since AB∥CD, AX will be a transversal

=> ∠BAO and ∠OXC will be co-interior angles

=> ∠BAO + ∠OXC = 180°

=> ∠OXC = 180 - 104 = 76°

since ∠OCX and ∠OCD form a line,

∠OCX = 180 - 116 = 64°

OXC forms a triangle

=> sum of angles = 180°

=> ∠OXC + ∠XCO + ∠COX = 180°

=> 76° + 64° + ∠COX = 180°

=> ∠COX = 180° - 140° = 40°

since x and ∠COX form a line,

x + ∠COX = 180°

=> x = 140°