The Consecutive Angles of a Parallelogram Are in the Ratio 3:6. Calculate the Measures of All the Angles of the Parallelogram.

Question

The consecutive angles of a parallelogram are in the ratio 3:6. Calculate the measures of all the angles of the parallelogram.

Sum

Solution

Let ABCD is a parallelogram in which AD || BC.
∠A and ∠B are consecutive angles:
∠A : ∠B = 3 : 6
∴ ∠A = 3x and ∠B = 6x
AD || BC and AB is the transversal.
⇒ ∠A + ∠B = 180° ....(Co-interior angles are supplementary)
⇒ 3x + 6x = 180°
⇒ 9x = 180°
⇒ x = 20
∴ ∠A = 3 x 20° = 60° and ∠B = 6 x 20° = 120°
Since opposite angles of a parallelogram are equal.
∴ ∠C =∠A = 60° and ∠D = ∠B = 120°.

shaalaa.com

Properties of a Parallelogram - Property: The Opposite Angles of a Parallelogram Are of Equal Measure.

Is there an error in this question or solution?

RELATED QUESTIONS

In a parallelogram `square`ABCD, If ∠A = (3x + 12)°, ∠B = (2x - 32)° then find the value of x and then find the measures of ∠C and ∠D.

In the following figure, ABCD and PQRS are two parallelograms such that ∠D = 120° and ∠Q = 70°.
Find the value of x.

In case of a parallelogram
prove that:
(i) The bisectors of any two adjacent angles intersect at 90^o.
(ii) The bisectors of the opposite angles are parallel to each other.

In the given figure, AP is the bisector of ∠A and CQ is the bisector of ∠C of parallelogram ABCD.

Prove that APCQ is a parallelogram.