Question

In the given figure PQ and RS are two lines intersecting each other at point 'O'.If angle ROT is 90 degree, find the value of x,y,z. ​

please give the ans as fast as possible.

Answer 1

angle ROT =90
as given in diagram,
angle POR=2x
POR + ROQ= 180 (ANGLES IN A LINEAR PAIR)
2x + ROT +ROQ =180
2x+90 +x= 180
3x=180-90
3x=90
x=90/3
x=30
ROQ =90 +30 =120
z=ROQ =120 (vertically opposite angles)
y=POR =2x30 =60 (vertically opposite angles)

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Answer 2

For the given figure, the values of $x,y,$ and $z$ are:

• x = 30°,
• y = 60°,
• z = 120°.

Given,

Refer figure.

∠POR = $2x,$

∠POS = $z,$

∠SOQ = $y,$

∠ROT = 90°, and

∠TOQ = $x.$

To find,

$x, y , and, z.$

Solution,

From the given figure, it can be seen that the two lines PQ and RS are intersecting at a point O.

Now, we can see that in the given figure, there are some pairs of angles formed. These are as follows.

• Vertically opposite angles

∠POR = ∠SOQ     ...(1)

∠POS = ∠ROQ     ...(2)

• Linear pair

∠ROQ and ∠QOS     (∵ RS is a straight line)

⇒ ∠ROQ + ∠QOS = 180°

⇒ ∠ROT + ∠TOQ + ∠QOS = 180°

$\implies 90+x+y=180$

Simplifying the above equation,

$x+y=180-90$

$\implies x+y=90$     ...(3)

Now, from the given values of angles, we can see that,

From (1),

$2x=y$

Or, $y=2x$

Substituting the above value of $y$ in eq. (3), we get,

$x+2x=90$

$\implies 3x=90$

⇒ x = 30°.     ...(4)

$\because y=2x$

$\implies y=2(30)=60$

⇒ y = 60°.

Also, from (2), we have,

$z=90+x$

$\implies z=90+30$     (∵ x = 30, from eq. 4)

⇒ z = 120°.

Therefore, for the given figure, the values of $x,y,$ and $z$ are:

• x = 30°,
• y = 60°,
• z = 120°.

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