Question

In the figure,seg AB ~ seg AD ,seg BC ~ BD , angle BAD = 80° angle BCD= 65° .Find the value of x and y and z​

Answer 1

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Answer 2

Answer: The values are,

∠x = 50°

∠y = 50°

∠z = 65°

Step-by-step explanation:

Given: seg AB ≅ seg AD ,seg BC ≅ BD , angle BAD = 80° angle BCD= 65°

To find : value of x, y and z

We have, seg AB ≅ seg AD,

therefore, ∠y = ∠x      ∵angles opposite to equal sides are equal.

Now, in ΔABD, ∠x + ∠y + 80° = 180°  (sum of angles in a triangle = 180°)

therefore,  ∠x + ∠x + 80° = 180°      ∵∠y = ∠x

i.e,  2∠x + 80° = 180°

On solving the above, we get ∠x = ∠y = 50°

Now, to find  ∠z,

Since, seg BC ≅ BD,

therefore, ∠z = ∠BCD = 65°      (angles opposite to equal sides are equal)

Hence the values are,

∠x = 50°

∠y = 50°

∠z = 65°