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
Fill in the blanks:
Two angles forming a linear pair are ______
Are the ray PM and PT opposite rays? Give reasons for your answer.
There are six angles at a point. One of them is 45° and the other five angles are all equal. What is the measure of all the five angles?
The measure of ∠BOC is
In the following figure, a = 40°. The value of b is ______.
In the following figure, PQ || RS and a : b = 3 : 2. Then, f is equal to ______.
What is the type of other angle of a linear pair if one of its angle is acute?
