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Answer:
82
Step-by-step explanation:
because diagonals are equal in quadrilater
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Rewritten by : Barada
In the given quadrilateral ABCD, where AB = AD and BC = DC, and with angles [tex]\( \angle ABD = 35^\circ \)[/tex], [tex]\( \angle BCD = 82^\circ \)[/tex], and [tex]\( \angle BDC = y \)[/tex], the value of angle [tex]\( \angle BAD \)[/tex] is 110°.
To find the value of angle x, we can use the properties of quadrilaterals, specifically the properties of a kite, which is a type of quadrilateral where adjacent sides are equal in length.
Given that AB = AD and BC = DC, we have two pairs of adjacent sides equal in length, suggesting that ABCD could be a kite. Additionally, [tex]\( \angle ABD = \angle ADB \)[/tex] and [tex]\( \angle BCD = \angle DBC \)[/tex] because opposite angles in a quadrilateral sum up to 180°. This is a property of all quadrilaterals.
Now, let's focus on triangle ABD. We know that the sum of angles in a triangle is 180°. So, [tex]\( \angle ABD + \angle ADB + \angle BAD = 180^\circ \)[/tex]. Substituting the given values, we have 35° + 35° + x = 180°. Simplifying, we get 70° + x = 180°, and solving for x gives us x = 110°.
Thus, the value of angle x is 110°, and this is obtained by applying the properties of quadrilaterals and triangles, particularly focusing on the kite shape formed by ABCD and using the fact that the sum of angles in a triangle is 180°.
