in an isoseles triangle the verted angle is twice of either base angle find the value of each angle
Answers
An isosceles triangle has two sides of equal length. Likewise, the opposite angles of the sides are the same
So lets assume each angle be
x
and the bigger angle be
2
x
(since it is twice the base angle)
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Now, we know that sum of the angles in a triangle is 180 degree
So,
→
2
x
+
x
+
x
=
180
∘
→
4
x
=
180
∘
→
x
=
180
4
⇒
x
=
45
∘
Now the other angle is
2
x
which is
45
×
2
=
90
∘
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Answer :
- Vertex angle is 90⁰
Given :
- In an iscoscles triangle the vertex angles is twice of either base angles
To find :
- The Value of each angle
Solution :
- Let the angle be x
Given, the vertex angle is twice of either base angle so,
- 2x
We know that
- Sum of all angles in a triangle is equal to 180⁰
According to Question,
➞ 2x + x + x = 180⁰
➞ 4x = 180⁰
➞ x = 180/4
➞ x = 45⁰
Finding the value of each angle :
➞ 2x = 2(45) = 90⁰
Hence , Vertex angle is 90⁰
Verification :
➞ 2x + x + x = 180⁰
➞ 2(45⁰) + 45⁰ + 45⁰ = 180⁰
➞ 90⁰ + 45⁰ + 45⁰ = 180⁰
➞ 180⁰ = 180⁰
Hence , Verified.