Find all the angles of an equilateral triangle.
Solution:
Consider an equilateral triangle ABC
We have to find all the angles of an equilateral triangle.
We know that in an equilateral triangle all the sides are equal.
So, AB = BC = AC
We know that angles opposite to equal sides are equal.
Since AB = AC, ∠C = ∠B
Let ∠C = ∠B = a -------------- (1)
Similarly, BC = BA
So, ∠A = ∠C ----------------- (2)
From (1) and (2),
∠A = ∠B = ∠C = a
Considering triangle ABC,
∠A + ∠B + ∠C = 180°
a + a + a = 180°
3a = 180°
a = 180°/3
a = 60°
Therefore, ∠A = ∠B = ∠C = 60°
✦ Try This: In the adjoining figure, if PQ = PR and QS = RT then ∆PST is
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7
NCERT Exemplar Class 9 Maths Exercise 7.4 Problem 1
Find all the angles of an equilateral triangle
Summary:
An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. All the angles of an equilateral triangle is 60°
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