Question

In the figure given below, ABCD is a parallelogram in which angle BAD = 75° and angle DBC = 60°. Calculate the measures of the following angles:-
(A). Angle ADB
(B). Angle ABD
(C). Angle CDB

Answer 1

HINT:- Before solving this question, we must know about transversal and TRANSVERSAL: A transversal is a line that intersects two or more lines (that are often parallel).

Here, ‘l’ and ‘m’ are parallel lines and ‘t’ is the transversal.

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°

NOTE:- Let us now know about some more angles formed when a transversal cuts two parallel lines.
VERTICALLY OPPOSITE ANGLES: A pair of vertically opposite angles is always equal.
SUPPLEMENTARY ANGLES: A pair of angles that lie on a straight line, whose sum is 180°
CORRESPONDING ANGLES: A pair of corresponding angles is always equal.
ALTERNATE EXTERIOR ANGLES: A pair of alternate exterior angles is always equal.
CONSECUTIVE INTERIOR ANGLES: The sum of a pair of consecutive interior angles is always 180°.