Advertisements
Advertisements
Question
In the given figure, lines PQ, MN, and RS intersect at O. If x : y = 1 : 2 and z = 90°, find ∠ROM and ∠POR.
Advertisements
Solution
In the figure, lines PQ, MN and Rs are intersecting each other at O
x : y = 1 : 2, z = 90°
∠MOQ = ∠PON = z .......(Vertically opposite angles)
Now, RS is a straight line
∴ x + z + y = 180°
⇒ x + y + 90° = 180° .........(∵ z = 90°)
⇒ x + y = 180°− 90° = 90°
But x : y = 1 : 2
Let x = a then y = 2a
∴ a + 2a = 90°
⇒ 3a = 90°
⇒ a =`(90°)/3` = 30°
∴ x = 30° and y = 2a = 2 × 30° = 60°
Now, ∠ROM = y = 60°
and ∠POR = ∠SOQ ..........(Vertically opposite angles)
= x = 30°
APPEARS IN
RELATED QUESTIONS
In the below fig, POQ is a line. Ray OR is perpendicular to line OS is another ray lying
between rays OP and OR. Prove that ∠ROS = 1 (∠QOS − ∠POS).
statement are true and false
If angles forming a linear pair are equal, then each of these angles is of measure 90°.
If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes.
In the given figure, AB || CD || EF and GH || KL. The measure of ∠HKL is
State, true or false:
An infinite number of straight lines can be drawn through a given point.
In the given figure, AB is perpendicular to BC at B.
Find:
(i) the value of x.
(ii) the complement of angle x.
Write the complement of 25°
Write the supplement of 100°
Write the supplement of 0°
In the given figure, find the measure of the unknown angles:
