Question

use the given information in the fallowing figure to find the value of x​

Answer 1

GIVEN :-

• ∠A = 80°.
• ∠B = 56°.
• ∠C = 3x - 6°.
• Exterior angle , ∠ADE = 70°.

TO FIND :-

⇒∠D + ∠ADE = 180°. [Linear Pair]

⇒∠D = 180° - ∠ADE

⇒∠D = 180° - 70°

⇒∠D = 110°.

Hence the value of ∠D is 110°.

Now in quadrilateral ABCD , By angle sum property.

⇒ ∠A + ∠B + ∠C + ∠D = 360°.

⇒ 80° + 56° + (3x - 6)° + 110° = 360°.

⇒246° + (3x - 6)° = 360°.

⇒ 240° + 3x = 360°.

⇒ 3x = 360° - 240°.

⇒ 3x = 120°

⇒ x = 120°/3

⇒ x = 40°.

Hence the required value of x is 40°.