Question

In Fig. 8.31, OA and OB are opposite rays:
(i) If x = 25°, what is the value of y?
(ii) If y = 35°, what is the value of x?

Answer 1

i) y=50

ii) x =35

it is clear that the given fig. is linear pair

therefore sum of both angle will be 180°

=>( 3x) +(2y+5) = 180

=>3x + 2y =175

now for x=25

i) 3×25 + 2y= 175

=>75+ 2y= 175

=>2y=100

=>y= 50

ii) for y=35

=>3x + 2×35=175

=>3x + 70=175

=>3x= 105

=>x=35

Answer 2

(i) y = 50°

(ii) x = 35°

Step-by-step explanation:

See the given diagram attached.

Angles ∠ AOC and ∠ BOC are supplementary angles as AOB is a straight line.

So, ∠ AOC + ∠ BOC = 180°

⇒ (2y + 5)° + 3x° = 180°

⇒ 2y° + 3x° = 175° ............. (1)

(i) Now, for x = 25°, from equation (1) we get,

2y° + 75° = 175°

⇒ 2y° = 100°

⇒ y° = 50° (Answer)

(ii) Again, for y = 35°, from equation (1) we get

70° + 3x° = 175°

⇒ 3x° = 105°

⇒ x° = 35° (Answer)