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
If an angle is 30° more than one half of its complement, find the measure of the angle.
In the given below fig, rays OA, OB, OC, OP and 0E have the common end point O. Show
that ∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360°.
statement are true and false
If angles forming a linear pair are equal, then each of these angles is of measure 90°.
Fill in the blank so as to make the following statement true:
If one angle of a linear pair is acute, then its other angle will be _____
The supplement of a right angle is ..............
Write the supplement of an angle of measure 2y°.
In the given figure, if CP || DQ, then the measure of x is
In the following figure, ∠AOB and ∠AOC are adjacent angles? Give the reason for your answer.
In the given figure, BAC is a straight line.
Find:
(i) x
(ii) ∠AOB
(iii) ∠BOC
In the following figure, ∠AOB and ∠AOC are adjacent angles? Give the reason for your answer.
