Question

in an adjoining figure ABCD is a parallelogram in which ∠BAD=75 degree and ∠DBC=60 degree , Find ∠ADB

Answer 1

Complete step-by-step solution -

The different angles formed when a transversal cuts two parallel lines are mentioned below in the hint.

We should also know about the angle sum property of triangles.

ANGLE SUM PROPERTY: The sum of the angles of a triangle is 180°.

GIVEN: ABCD is a parallelogram

Angle BAD = 75°

Angle DBC = 60°

TO FIND: Angle ADB

Angle ABD

Angle CDB

(a).Measure of angle ADB.

Angle ADB = Angle DBC (alternate interior angles)

ALTERNATE INTERIOR ANGLES: A pair of alternate interior angles is always equal.

Therefore, angle ADB = 60°

(b)Measure of angle ABD.

Now, as we know that the measure of angle ADB is 60°, we can find the measure of the angles ABD using the angle sum property of triangles.

In ∆ABD,

Angle A + Angle B + Angle D = 180° (angle sum property of triangle)

ANGLE SUM PROPERTY: The sum of the angles of a triangle is 180°

75° + Angle B + 60° = 180°

135°+ Angle B = 180°

Angle B = 180° - 135°

Angle B = 45°

Therefore, angle ABD = 45°

(c) Measure of angle CDB

Angle CDB = Angle ABD (alternate interior angles)

ALTERNATE INTERIOR ANGLES: A pair of alternate interior angles is always equal.

Therefore, angle CDB = 45°