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
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 _____
If two straight lines intersect each other, prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.
The complement of an acute angle is ..............
Write the supplement of an angle of measure 2y°.
In the given figure, if CP || DQ, then the measure of x is
State, true or false:
A line segment is the shortest distance between any two given points.
How many rays can be drawn through a fixed point O?
In the following figure, ∠AOB and ∠AOC are adjacent angles? Give the reason for your answer.
In the given figure. p° = q° = r°, find each.
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.
