Question

find x and y .......​

Answer 1

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Given :

ABCD is a quadrilateral .

AB is extended to a point D.

angle DAB = y°

angle BCD = x°

angle ADC = 120°

angle CBD = 100°

Required to find :

1. Measurement of angle DAB ( y)
2. Measurement of angle BCD (x)

Solution :

(please refer to the attachment carefully ).

It is given that In a quadrilateral ABCD , AB is extended to a point D

so , to find angle DAB we have to first find the measure of angle BCD.

hence,

2.(2nd part of required to find )

consider side AB which is extended to D.

when AB is extended to D it leads to the formation of the exterior angel named angle CBD = 100°

so, here we can find one angle using the exterior angle property.

hence ,

angle ABC + angle CBD = 180° ( Because they form a linear pair ).

angle ABC + 100° = 180°

angle ABC = 180° - 100°

angle ABC = 80°

therefore,

angle ABC = 80°

Now,

In quadrilateral ABCD ,

angle ABC + angle BCD = 180° ( because sum of two adjacent angles of a quadrilateral is supplementary ).

80° + angle BCD = 180°

angle BCD = 180° - 80°

angle BCD = 100°

Therefore,

measure of angle BCD = 100°

1. ( first part of required to find )

Now we have to find the value of angle DAB.

To find angle DAB we have to the property that is sum of all angles in a quadrilateral is 360°

so,

angle ABC + angle BCD + angle CDA + angle DAB = 360°

80° + 100° + 120° + angle DAB = 360°

300° + angle DAB = 360°

angle DAC = 360° - 300°

angle DAB = 60°

Therefore,

measure of angle DAB = 60°

measure of angle BCD = 100°

Note :

Remember there are multiple methods to solve this type of geometric questions.

so I strongly suggest you to go through the matter given above .

I will clear all your doubts..

Answer 2

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Given :

ABCD is a quadrilateral .

AB is extended to a point D.

angle DAB = y°

angle BCD = x°

angle ADC = 120°

angle CBD = 100°

Required to find :

Measurement of angle DAB ( y)

Measurement of angle BCD (x).

It is given that In a quadrilateral ABCD , AB is extended to a point D

so , to find angle DAB we have to first find the measure of angle BCD.

consider side AB which is extended to D.

when AB is extended to D it leads to the formation of the exterior angel named angle CBD = 100°

so, here we can find one angle using the exterior angle property.

hence ,

angle ABC + angle CBD = 180° ( Because they form a linear pair ).

angle ABC + 100° = 180°

angle ABC = 180° - 100°

angle ABC = 80°

therefore,

angle ABC = 80°

Now,

In quadrilateral ABCD ,

angle ABC + angle BCD = 180° ( because sum of two adjacent angles of a quadrilateral is supplementary ).

80° + angle BCD = 180°

angle BCD = 180° - 80°

angle BCD = 100°

Therefore,

measure of angle BCD = 100°

1. ( first part of required to find )

Now we have to find the value of angle DAB.

To find angle DAB we have to the property that is sum of all angles in a quadrilateral is 360°

so,

angle ABC + angle BCD + angle CDA + angle DAB = 360°

80° + 100° + 120° + angle DAB = 360°

300° + angle DAB = 360°

angle DAC = 360° - 300°

angle DAB = 60°

Therefore,

measure of angle DAB = 60°

measure of angle BCD = 100°