Math, asked by IndianDesisciene, 4 months ago

In the given figure ABCD, find the value of x

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Answered by Anonymous
3

Angle Sum Property Of Quadrilateral

The basic concept used in this question is angle sum property of quadrilateral. According to this property, sum of all interior angles of a triangle is always equals to 360°.

In order to solve this problem, firstly we will find 3 interior angles of the given quadrilateral using " linear pair property ". According to this property, sum of both angles on either side of a straight line on a ray is always equals to 180°.

These both angles are adjacent to each other and share a common arm.

So let's start our solution by finding interior angles of quadrilateral !

Finding angle C ( Interior )

⇝ ∠ DCB ( Interior ) + 70° = 180° ( Linear pair )

⇝ ∠ DCB = 180° - 70°

∠ DCB = 110°

Finding angle B ( Interior )

⇝ ∠ ABC ( Interior ) + 80° = 180° ( Linear pair )

⇝ ∠ ABC = 180° - 80°

∠ ABC = 100°

Finding angle A ( Interior )

⇝ ∠ BAD ( Interior ) + 70° = 180° ( Linear pair )

⇝ ∠ BAD = 180° - 70°

∠ BAD = 110°

Since, we have obtained 3 interior angles, now we will find interior angle D by using angle sum property of quadrilateral.

⟹ ∠ A + ∠ B + ∠ C + ∠ D = 360°

⟹ ∠ BAD + ∠ ABC + ∠ DCB + ∠ ADC = 360°

⟹ 110° + 100° + 110° + ∠ ADC = 360°

⟹ ∠ ADC = 360° - 100° - 110° - 110°

∠ ADC = 40°

Now since, we know that angle created either side of a line segment on a straight line is equals to 180° by linear pair property, we can find the value of x easily by using this concept.

↦ ∠ ADC + x = 180° ( Linear pair )

↦ 40° + x = 180°

↦ x = 180° - 40°

↦ x = 140°

Hence the required angle ' x ' is 140° .

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