Page 44 - Ganit Kaushal

Solved Examples

Ex 1. In each case, determine which angle is greater and why. X
(a) ∠AOB or ∠XOY
Y
(b) ∠AOB or ∠XOB A
(c) ∠XOB or ∠XOC (NCERT)

Sol. (a) ∠AOB is greater than ∠XOY. O B C
The two arms of ∠XOY lie within ∠AOB.
Also, after superimposing the initial arm OY on OB, the final arm OA A
lies after OX (see adjacent fig.). X

(b) ∠AOB is greater than ∠XOB.

The initial arm OB of the two angles is superimposed and the final
arm OA lies after OX. O B Y C
(c) ∠XOB and ∠XOC are equal angles.
Their common vertex and both arms exactly overlap each other.

Ex 2. In the given figure, which angle is greater: ∠XOY or ∠AOB? Give reasons. (NCERT)

X A

Y

O B
Sol. ∠XOY is greater than ∠AOB.
After superimposing the vertices and the initial arm OY on OB, we X A
observe that the final arm OX still lies after OA.

O Y B
Ex 3. Name the angles in the adjoining figure. C
D
Sol. The angles in the given figure are
∠ABC, ∠BCD, ∠CDA, and ∠DAB.
A B
Ex 4. In the adjoining figure, name the points:

(a) In the interior of ∠DOE. F
(b) In the exterior of ∠EOF. C E

(c) On the boundary of ∠EOF.
B
Sol. (a) The point in the interior of ∠DOE is A. A

(b) The points in the exterior of ∠EOF are C, A, and D. O D
(c) The points on the boundary of ∠EOF are E, O, B, and F.

42 Mathematics-6