Advertisements
Advertisements
प्रश्न
In the given figure, lines PQ, MN, and RS intersect at O. If x : y = 1 : 2 and z = 90°, find ∠ROM and ∠POR.
उत्तर
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
संबंधित प्रश्न
If an angle is 30° more than one half of its complement, find the measure of the angle.
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:
A ray stands on a line, then the sum of the two adjacent angles so formed is ______
The supplement of an acute angle is .................
Two straight lines AB and CD cut each other at O. If ∠BOD = 63°, then ∠BOC =
In the following figure, ∠AOB and ∠AOC are adjacent angles? Give the reason for your answer.
In the following figure, ∠AOB and ∠AOC are adjacent angles? Give the reason for your answer.
In the given figure, if x = 2y, find x and y
Write the complement of `1/2` of a right angle
Write the complement of `1/3` of 180°
