Question

in the given figure ABCD is a parallelogram find angle ADC and angle ABD =55°​

Answer 1

Given:

A parallelogram ABCD with angle ABD =55°​

To Find:

Angle ADC

Solution:

A parallelogram is a quadrilateral with two pairs of opposite sides parallel to one another.

Constructing a diagonal DB, we can divide the parallelogram into two triangles: DCB & ADB.

Since, DC ║AB and DB is the transversal,

∠ABD = ∠BDC = 55°​ (Alternate interior angles are equal)

Also, ∠ADB = ∠BDC = 55°

∠ADC = ∠ADB + ∠BDC= 110°

Hence, ∠ADC = 110°