Problems Involving Angles

Concept Explanation

Problems Involving Angles

Directional Questions : Direction is the information contained in the relative position of one point with respect to another point without the distance information. Directions may be either relative to some indicated reference or absolute according to some previously agreed upon frame of reference.

In these type of questions a statement is given describing the position and movement of an object or an individual. A successive follow-up of directions is formulated and the candidate is required to ascertain the final direction or the distance between two points. These questions are meant to judge the candidate,s ability to trace and follow correctly and sense the direction correctly.

The adjoining figure shows the four main directions (North N, South S, East E, West W) and four cardinal directions (North East NE, North West NW, South East SE, South West SW) to help the candidates know the directions.

Problems Involving Angles : In these type of question a person or an object starts moving at an angle or after moving in various directions turns at an angle.

When a person is facing towards north and he turns 360⁰ clockwise or anticlockwise he reaches to his starting direction always.

90⁰ + 90⁰ + 90⁰ + 90⁰= 360⁰

90⁰ + 90⁰ + 90⁰ + 45⁰=315⁰

90⁰ + 90⁰ + 90⁰=270⁰

90⁰ + 90⁰ + 45⁰=225⁰

90⁰ + 90⁰ =180⁰

90⁰ + 45⁰ =135⁰

45⁰ + 45⁰ =90⁰

Illustration : A man is facing west. He turns $large 45^{circ}$ in the direction and then another $large 180^{circ}$ in the same direction and then $large 270^{circ}$ in the anti-clockwise direction. Which direction is he facing now ?

A. South B. North-west C. West D. South-west

Answer: D

Solution : Clearly, the man initially faces in the direction west direction that is along OA as shown in the figure.

On moving $large 45^{circ}$ clockwise, he faces in the direction OB.

On further moving $large 180^{circ}$ clockwise, he faces in the direction OC.

Finally, on moving $large 270^{circ}$ anti-clockwise, he faces in the direction OD. which is South-west. .

Hence the correct option is D.

Illustration : Deepa moved a distance of 75 meters towards the north. She then turned to the left and walking for about 25 meters, turned left again and walked 80 meters. Finally , she turned to the right at an angle of $large 45^{circ}$ . In which directions was she moving finally?

A. North-east B. North-west C. South-east D. South-west

Answer : D

Solution : Let us draw a diagram depicting the movement of Deepa . Assume that Deepa started from A,

She moved 75 m towards the North and reached point B

She then turned left and walked 25 m and reached [point C.

She then turned left again and moved 80 m and reached point D.

Turning to the right at an angle of $large 45^{circ}$ , she was finally moving in the direction DE i.e., South-west.

Hence, the Correct Option is D.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Pankaj is facing in north , he turns 45⁰ clockwise and covers some distance , than turns in south direction and covers a distance of 9 km and than he turns in his right and covers a distance of 2 km and than moves in north direction and covers a distance of 5 km and than turns his left and covers a distance of 1 km. What is the distance covered by him when he turns 45⁰ clockwise ?
A. 3 km	B. 4 km	C. 5 km	D. 6 km
Right Option : C
View Explanation

Question : 2

A person is facing in north, he turns 135⁰ clockwise , in which direction he is facing now?
A. Northeast	B. Northwest	C. Southeast	D. Southwest
Right Option : C
View Explanation

Question : 3

Aadarsh is facing toward southwest , he turns 45⁰ anticlockwise, In which direction he is standing now?
A. East	B. West	C. North	D. South
Right Option : D
View Explanation