Question

Find the value of X in the given figure.


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Answer 1

Step-by-step explanation:

Given:-

Given attachment

exterior angle EAD = 140°

angle DCB = 120°

angle ABC = x°

angle ADC = 20°

To find:-

Find the value of x?

Solution:-

Method-1:-

From the given figure

exterior angle EAD = 140°

angle EAD and angle DAB are linear pair

angle EAD +angle DAB = 180°

=>140°+angle DAB = 180°

=>angle DAB = 180°-140°

angle DAB = 40°

and angle DCB = 120°

We know that

angle around a point = 360°

angle DCB +reflex angle DCB = 360°

=>120°+reflex angle DCB = 360°

=>reflex angle DCB = 360°-120°

reflex angle DCB = 240°

In a quadrilateral ABCD ,

We have ,

angle DAB =40°

angle ABC = x°

Reflex angle BCD =240°

angle ADC = 20°

we know that

The sum of all angles in a quadrilateral is 360°

=>angle DAB +angle ABC +angle ADC+reflex BCD

=>40°+x°+20°+240°=360°

=>300°+x° = 360°

=>x°=360°-300°

=>x°=60°

Method -2:-

Draw a Parallel line from the bisecting line C

angle DCB = 120°

angle FCB = 120°/2 = 60°

Then FG || AB and BC is a transversal then

angle FCB and angle ABC are the alternative interior angles

We know that

The alternative interior angles are equal when two parallel lines are interested by a transversal

angle FCB = angle ABC

=>60° = x°

x°=60°

Answer:-

The value of x°=60° for the given problem

Used formulae:-

• angle around a point = 360°

• The sum of two adjacent angles is 180° then they are called linear pair.

• The sum of all angles in a quadrilateral is 360°

• The alternative interior angles are equal when two parallel lines are interested by a transversal

Answer 2

x = 60°

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