Since, parallel RSTU is a rhombus. Thus, the is a residential property of rhombus the opposite angles have equal measure.
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Thus, m∠R = 120° =m∠T
Also, m∠U = m∠S
Let it it is in x°.
Angle sum residential property of parallelogram states that the sum of angles of a parallelogram is 360°.
m∠R + m∠T+ m∠U + m∠S = 360°
120 +!20 +x + x = 360
2x = 360 - 240
2x = 120
x = 60°
Thus, m∠U = m∠S = 60°
Also in Rhombus, each diagonal bisects two opposite internal angles.
Then , us is a diagonal line bisecting ∠U and also ∠S.
m∠RSU = 30° = m∠TSU
Thus, m∠RSU = 30°
A. It should be a parallelogram
The prize is "A. It must be a parallelogram" because every rhombus is a parallelogram.
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∠RSU=30° and also ∠T=120°
Given a parallel RSTU and m∠T = 120°. We have actually to uncover the measure up of angle m∠RSU.
As opposite angles of parallelogram are equal
By edge sum residential property of triangle which says that amount of all the angles of triangle is 180°
⇒ m∠RSU+120°+m∠RSU=180° (∵RSTU is a rhombus.)
⇒ 2m∠RSU=60° ⇒ m∠RSU=30°
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