Question

two lines l and m intersecting each other at o then find angles x,y,z​

Answer 1

• x is of 70°.
• y is of 120°.
• z is of 120°.

Step-by-step explanation:

To find:-

• Value of x, y and z.

Solution:-

We know that,

Sum of all angles forms on straight line is 180°. This statement is also known as linear pair.

So,

➝ 60° + y = 180°

➝ y = 180° - 60°

➝ y = 120°

We also know that,

If two lines bisect or intersect there vertical opposite angles are equal. This statement is also known as Vertically opposite angles.

So,

x = 60° [Vertically opposite angle]

y = z = 120° [Vertically opposite angles]

Therefore,

Measure of x, y and z are 60°, 120° and 120° respectively.

Answer 2

Question-

Two lines l and m intersecting each other at O, then find angles x, y, z.

Answer-

The value of :

• x = 60°

• y = 120°

• z = 120°

Solution-

In the given figure, 60° and y are linear angles.

We know that sum of linear angles is 180°.

So, we can say-

y + 60 = 180

Subtract 60 from both sides.

➳ y + 60 - 60 = 180 - 60

➳ y = 120 $\red{★}$

y = 120°

In the given figure, l and m intersect each other.

So, the vertically opposite angle are equal.

Therefore,

x = 60° $\red{★}$

y = x = 120° $\red{★}$

Confused??

Verification-

We know that a complete angle = 360°

So,

60° + x + y + z = 360°

Putting the values of x, y, z,

➳ 60° + 60° + 120° + 120° = 360°

➳ 360° = 360°

So, L.H.S = R.H.S.

Hence, verified.

Done

Have a query regarding “linear angles” and “vertically opposite angles”??

Linear angles-

The adjacent angles, formed when two lines intersect, are know as linear angles. The sum of two linear angles is 180°.

Vertically opposite angles-

When two lines intersect, the pair of angles, which lie on the opposite sides of the point of intersection, are called vertically opposite angles.

Hope this helps you.

Have a nice day.