Q1 of 12 Page 84

In the given figure three lines and intersecting at O. Find the values of x, y and z it is being given that x : y : z = 2 : 3 : 5

From the given, the three angles are x,y,z


If the two lines intersect at a point then its vertically opposite angles are equal.


∴ A = x, B = z and C = y


We know that,The sum of all the angles around at a point is equal to 360°


∴ A + B + C + x + y + z = 360°


⇒ x + y + z + x + y + z = 360°


⇒ 2x + 2y + 2z = 360°


⇒ 2(x + y + z) = 360°


⇒ (x + y + z) =


⇒ x + y + z = 180° ------(1)


Given that, x : y : z = 2 : 3 : 5


Let x = 2m,y = 3m,z = 5m (∵ m = constant)


Substitute these values in equation (1) we get


2m + 3m + 5m = 180


10m = 180


m =


∴ m = 18


Substituting m = 18 in x,y,z


x = 2m,x = 2(18) = 36°


y = 3m,y = 3(18) = 54°


z = 5m,z = 5(18) = 90°


∴ x = 36°,y = 54°,z = 90°


More from this chapter

All 12 →
3

State whether the following statements are true or false :

i. A ray has no end point.


ii. Line is the same as line .


iii. A ray is same as the ray


iv. A line has a define length.


v. A plane has length and breadth but no thickness.


vi. Two distinct points always determine a unique line.


vii. Two lines may intersect in two points.


viii. Two intersecting lines cannot both be parallel to the same line.

4

What is the angle between two hands of a clock when the time in the clock is

(a) 9’O clock


(b) 6’O clock


(c) 7:00 PM

 2

Find the value of x in the following figures.

i. ii.


iii. iv.

3

In the given figure lines and intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.