Question

In a rhombus PQRS ,diagonal PR is equal to side QR. Find the measure of all the angles

Answer 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°.

sorry angles k name different h
but this is thee ryt wy to solve this
question