Question

If the ratio of measures of two adjacent angles of a parallelogram is 1:2 find the measures of all the angles of a parallelogram.​

Answer 1

Answer :-

• ∠A = 60°
• ∠B = 120°
• ∠C = 60°
• ∠D = 120°

Given :-

• Ratio of adjacent angles of a parallelogram = 1 : 2 (∠A : ∠B)

To Find :-

• All four angles of parallelogram (∠A, ∠B, ∠C and  ∠D)

Explanation :-

Let the adjacent angles to be 1x and 2x respectively.

➤ As AD || BC and AB as transversal,

$\rm \implies \angle A + \angle B = 180^{\circ} \qquad \bold{[Angle \: on \: the \: same \: transversal]}$

$\rm \implies 1x + 2x = 180^{\circ}$

$\rm \implies 3x = 180^{\circ}$

$\rm \implies x = \dfrac{180^{\circ}}{3}$

$\underline { \boxed { \rm \implies \bold { x = 60^{\circ} }}}$

Now, substituting the value of x

$\rm \implies \angle A = 1x = 1(60^{\circ}) = \bold { 60^{\circ}}$

$\rm \implies \angle B = 2x = 2(60^{\circ}) = \bold { 120^{\circ}}$

As we know, In a quadrilateral the opposite angles are equal.

$\rm \implies \bold { \angle A = \angle C = 60^{\circ} } \qquad [Opposite \: Angles \: of \; \parallel gm]$

$\rm \implies \bold { \angle B = \angle D = 120^{\circ} } \qquad [Opposite \: Angles \: of \; \parallel gm]$

Hence, all four angles of the parallelogram are 60°, 120°, 60° and 120°

@Agamsain