Question

6. In the figure, PQ|| MN. Find the value of x.


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Answer 1

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Answer 2

Answer:

x = 230°

Step-by-step explanation:

Given :

• MN and PQ are parallel lines .

• ange M = 110° , and angle p = 120°

To Find :

• x = ?

Construction :

Draw a line lb bisecting angle O.

Procedure :

(Before proceeding , please refer to the attached file)

It is given that the the two lines MN and PQ are parallel to each other.

According to theorem of parallel lines :

Two lines which are parallel to the same given line e parallel to each other.

So ,

$\sf \: MN\parallel PQ\\\\ \sf \: LB\parallel \: PQ \\\\ \sf \:LB\parallel MN$

Now , all properties of parallel lines could be performed here.

$\sf \angle1 = \angle \: p = 120 ^{ \circ} \longrightarrow \: \: (alternate \: angles)$

$\sf \angle2 = \angle \: m = 110^{ \circ} \longrightarrow \: \: (alternate \: angles)$

$\sf \angle \: o = 120 ^{ \circ} + 110 ^{ \circ}$

$\sf \: \angle \: o = x = 230^{ \circ}$