Question

A parallelogram has one angle that measures 60 what are the measures of the other three angles in a parallelogram

Answer 1

Hi

We know that opposite angles of a //gm are equal

Let one of the angle be=x

60+60+x+x=360

2x=360-120
2x=240
x=120
so, angles are

60,60,120 & 120

Answer 2

Let's give name to the parallelogram.

ABCD is a parallelogram.

【Refer to the attachment】

Given angles »

∠A = 60°
∠B = ∠z............(ii)
∠C = ∠x...........(i)
∠D = ∠y...........(iii)

(i)

We know,

In a parallelogram, opposite sides are equal.

∴ ∠A = ∠C

⇒ 60° = ∠x

Hence, ∠x = 60°

(ii)

We know, In a parallelogram,

Sum of adjacent ∠s = 180°

∴ ∠A + ∠B = 180°

⇒ 60° + ∠z = 180°

⇒ ∠z = 180° - 60°

⇒ ∠z = 120°

Hence, ∠z = 120°

(iii)

We know, In a parallelogram,

Sum of adjacent ∠s = 180°

∴ ∠A + ∠D = 180°

⇒ 60° + ∠y = 180°

⇒ ∠y = 180° - 60°

⇒ ∠y = 120°

Hence, the four angles of parallelogram are

60°, 60°, 120° & 120°

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