Math, asked by rekhatiwari35, 11 months ago

in a rhombus pqrs diagonal PR is equals to side QR find the measures of angles of a rhombus pqrs​

Answers

Answered by Anonymous
1

ABCD is a Rhombus ⇒ AC = BC ------------ (1) [Given data]

BC = AB --------------- (2) [Sides of the Rhombus]

From equations (1) and (2)

AC = BC = AB

⇒ ΔABC is an equilateral triangle.

So, <ABC = 60°,

<BCA = 60° ------------------------- (3)

<CAB = 60° --------------------------(4)

Similarly, in ΔADC, AD = DC [Sides of a rhombus]

AD = BC

But BC = AC

∴ AD = AC

∴ AD = DC = AC

∴ DADC is an equilateral triangle.

⇒ <CAD = 60° ---------------- (5)

⇒ <ADC = 60°

⇒ <DCA = 60° ----------------- (6)

From equations (3) and (6), we get <BCA + <DCA = 60° + 60° = 120°

∴ <C = 120°

From equations (4) and (5), <CAB + <CAD = 60° + 60° = 120°

<A = 120°.

Therefore, four angles of the rhombus are 120°, 60°, 120°, 60°.

Answered by devilsmind1302
1

Answer:

Step-by-step explanation:

In rhombus PQRS the diagonal PR equals the side QR ...(GIVEN)

Now consider only Δ PQR

PR≅QR

hence its an isoceles triangle

thus,∠RPQ≅∠PRQ ......(1)

Now as the given quadrilateral is a rhombus all the side are congruent

thus QR ≅PS

Thus considering the ΔPRS

PS≅PR..........(∵QR≅PR And QR≅PS)

thus ∠PSR =PRQ......(2)

from 1 and 2

∠PSR ≅ ∠PQR

now in rhombus opposite angles are congruent

hence by angle addition rule of quadrilateral

∠P+∠Q+∠R+∠S =360

from 3

2∠P + 2∠Q = 360   (P≅R AND S≅Q)

Thus P+Q=180

but from given statement we get the values

as ∠P=120°

∠Q=60

∠R=120

∠S=60

Similar questions