In the given figure ABCD, find the value of x
Answers
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°