One of the diagonals of a rhombus and its sides are equal. Find the angles of the rhombus.
Solution:
Given, one of the diagonals of a rhombus and its sides are equal.
We have to find the angles of the rhombus.
Let PQRS be a rhombus
Let the diagonal be PR
Given, PR is equal to the side of the rhombus
So, PR = PQ
In a rhombus, all sides are equal.
PQ = QR = RS = PS
From the figure,
The triangles PQR and PRS are equilateral.
In an equilateral triangle, all the sides are equal and each of its angles is equal to 60 degrees.
∠1 = ∠2 = ∠3 = ∠4 = 60°
So, ∠P = ∠1 + ∠2
= 60° + 60°
∠P = 120°
We know, ∠P = ∠R = 120°
∠S = ∠Q = 60°
Therefore, the angles of the rhombus are 120°, 60°, 120° and 60°.
✦ Try This: Diagonals of rectangle bisect each other at (a) 90°, (b) 60°, (c) 180°, (d) 120°
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 35
One of the diagonals of a rhombus and its sides are equal. Find the angles of the rhombus.
Summary:
One of the diagonals of a rhombus and its sides are equal. The angles of the rhombus are 120°, 60°, 120° and 60°.
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