Mathematics
In the given figure, ABCD is a parallelogram. Side DC is produced to E and ∠BCE = 105°. Calculate ∠A, ∠B, ∠C and ∠D.
Answer
Given,
∠BCE = 105°
ABCD is a parallelogram.
⇒ ∠BCE + ∠BCD = 180° [Linear pairs]
⇒ ∠BCD = 180° - ∠BCE
⇒ ∠BCD = 180° - 105°
⇒ ∠BCD = 75°.
⇒ ∠A = ∠BCD = 75° [∵ opposite angles of a parallelogram are equal]
⇒ ∠A + ∠B = 180° [∵ AD ∥ BC and sum of Co-Interior angles is 180°]
⇒ ∠B = 180° - ∠A
⇒ ∠B = 180° - 75°
⇒ ∠B = 105°
⇒ ∠D = ∠B = 105° [∵ opposite angles of a parallelogram are equal]
Hence, ∠A = 75°, ∠C = 75°, ∠B = 105° and ∠D = 105°.
Related Questions
In the given figure, ABCD is a parallelogram in which ∠A = 70°. Calculate ∠B, ∠C, ∠D.
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
In the adjoining figure, ABCD is a parallelogram in which ∠BAD = 70° and ∠CBD = 50°. Calculate :
(i) ∠ADB
(ii) ∠CDB.
In the given figure, ABCD is a rhombus in which ∠A = 72°. If ∠CBD = x°, find the value of x.
