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.
Advertisements
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
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°.
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 _____
Write the complement of an angle of measure x°.
If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes.
Two straight lines AB and CD cut each other at O. If ∠BOD = 63°, then ∠BOC =
Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is
State, true or false:
A ray has one endpoint and a line segment has two end-points.
State, true or false:
An infinite number of straight lines can be drawn through a given point.
In the following figure, ∠AOB and ∠AOC are adjacent angles? Give the reason for your answer.
AB, CD and EF are three lines intersecting at the same point.
(i) Find x, if y = 45° and z = 90°.
(ii) Find a, if x = 3a, y = 5x and r = 6x.
