What is the measure of ∠ADC in quadrilateral ABCD?

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Question:

What is the measure of ∠ADC in quadrilateral ABCD?

It is only possible when the value of x is 115 degrees since side AB and CD are congruent. Thus, the value of ∠ADC is 115 degrees.

ABCD is the quadrilateral given in the question in which AD is parallel to BC, and AB is equal to CD. The value of angle BAC is given 115 degrees.

We need to determine the value of the ∠ADC.

Now,

Let us assume the value of ∠ADC is x.

The exterior angle of C and the ∠CDA are alternate interior angles. Thus, the value of the exterior angle of C is also x.

We know that sum of interior and exterior angles is always 180 degrees.

Thus, the value of ∠DCB is (180-x).

The exterior angle of B and the ∠BAD are alternate interior angles. Thus, the value of the exterior angle of B is also 115 degrees.

Thus, the value of ∠ABC is (180-115) which is equal to 65 degrees.

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Now, the sum of all the angles of the quadrilateral is always equal to 360 degrees.

Therefore,