Advertisements
Advertisements
Question
In the following figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠QOS measures ______.
Options
150°
75°
45°
60°
Advertisements
Solution
In the following figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠QOS measures 75°.
Explanation:
Since ∠POR and ∠QOS are in the ratio 1 : 5.
Let angles will be x and 5x, respectively.
We know that, the sum of angles forming linear pair is 180°.
∴ ∠POR + ∠ROS + ∠QOS = 180°
⇒ x + 90° + 5x = 180°
⇒ 6x = 180° – 90°
⇒ 6x = 90°
⇒ x = `90^circ/6`
⇒ x = 15°
∴ ∠QOS = 5x = 5 × 15°
⇒ ∠QOS = 75°
APPEARS IN
RELATED QUESTIONS
Indicate which pairs of angles are: Linear pairs.
Fill in the blanks:
Two angles forming a linear pair are ______
One angle of a linear pair is a right angle. What can you say about the other angle?
Find the value of y
Two angles are in the ratio 11 : 25. If they are linear pair, find the angles
The angle which makes a linear pair with an angle of 61° is of ______.
In the following figure, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to ______.
Two supplementary angles always form a linear pair.
In the following figure, write, if any, (i) each pair of vertically opposite angles, and (ii) each linear pair.
