Question

Parallelogram RSTU is a rhombus. m∠R = 120°

What is m∠T = 120



(What is m∠RSU?)

Answer 1

m∠RSU = 30°

Explanation:

Given Parallelogram RSTU is a rhombus. and m∠R = 120°

We have to find m∠RSU.

Since, Parallelogram RSTU is a rhombus. thus, it is a property of rhombus that opposite angles have equal measure.

Thus, m∠R = 120° =m∠T

Also, m∠U = m∠S

Let it be x°.

Angle sum 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 interior angles.

Then , US is a diagonal bisecting ∠U and ∠S.

m∠RSU = 30° = m∠TSU

Thus, m∠RSU = 30°

Answer 2

∠RSU=30° and ∠T=120°

Explanation:

Given a parallelogram RSTU and m∠T = 120°. We have to find the measure of angle m∠RSU.

As opposite angles of parallelogram are equal

⇒ m∠R=m∠T=120°

In ΔRUS,

By angle sum property of triangle which states that sum of all the angles of triangle is 180°

m∠RUS+m∠URS+m∠RSU=180°

⇒ m∠RSU+120°+m∠RSU=180° (∵RSTU is a rhombus.)

⇒ 120°+2m∠RSU=180°

⇒ 2m∠RSU=60° ⇒ m∠RSU=30°