如何找到三角形中缺失的角度？

三角形是几何图形。它是一个具有三个边（即三个顶点和三个边）的多边形，它在三角形中的内角之和为 180 ^o 。三角形主要分为三种。他们是-

1. 等边三角形——等边三角形的所有内角都相同。即，∠A=∠B=∠C=60 ^o 。其中 A,B,C 是内角。
2. 等腰三角形——它是一个三角形，两条边等长，各自的角度也相等。即，两个内角相等。
3. 不等边三角形——不等边三角形有三个内角不同的边，但这些内角的总和是 180^度。

如何找到三角形中缺失的角度？

根据角度和属性，三角形的所有内角之和为 180°。

∠a + ∠b + ∠c = 180°

让我们看看在三角形中寻找缺失角的不同场景。

示例问题

问题1：给定三角形中缺少的角度是多少？

解决方案：

We know that the sum of interior angles in a triangle is 180^o.

So, 70^o + 60^o + x = 180^o

130^o + x = 180^o

x = 180^o – 130^o

x = 50^o

So the missing angle in the given triangle is 50^o.

问题2：在给定的直角三角形中找到缺失的角度？

解决方案：

We know that in a right angled triangle one angle should be 90^o and other two angles sum should be 90^o.

So, 45^o + x = 90^o

x = 90^o – 45^o

x = 45^o

So the missing angle in the given right angled triangle is 45^o.

问题 3：在给定的等腰三角形中找到缺失的角度？

解决方案：

The given triangle is isosceles triangles which indicates that it has two sides of equal length and two equal angles.

So in this case we can find two angles of a triangle when one angle is given.

From the above statements x=y (Equation-1) and

We know that the sum of interior angles in a triangle is 180^o.

So, 30^o + x + y = 180^o

30^o + x + x = 180^o

30^o + 2x = 180^o

2x = 180^o – 30^o

2x = 150^o

x = 150^o/2

x = 75^o

Form equation-1 y = 75^o

So the missing angles in the given triangle are 75^o, 75^o.

在三角形中，与该边相对的任何角度的内角和外角之和等于180 ^° 。即使在某些情况下，我们也可以在问题陈述中找到外角来代替内角。所以我们可以通过公式找到内角 -

Interior angle = 180^o – Exterior angle

问题 4：给定三角形中缺少的角是多少？

解决方案：

Given

One interior angle = 60^o

Other exterior angle = 130^o

From exterior angle we can find interior angle by subtraction the exterior angle from 180^o

Interior angle = 180^o – 130^o

                      = 50^o

Now we have two angle we can find third angle by subtracting the summation of two angles from 180^o

60^o + 50^o + x = 180^o

110^o + x = 180^o

x = 180^o – 110^o

x = 70^o

The missing angle in this triangle is 70^o

问题 5：求给定等边三角形的角

解决方案：

The given triangle is an equilateral triangle

So not only the length of all sides are equal but also the angles are also equal.

∠x = ∠y = ∠z (Equation-1)

We know that sum of interior angles is 180^o

So x + y + z = 180^o

x + x + x = 180^o   (As all angles are same)

3x = 180^o

x = 180^o/3

x = 60^o

From equation-1 y = 60^o and z = 60^o

The missing angles in the given equilateral triangle are 60^o, 60^o, 60^o

这些都是在三角形中找到缺失角的所有可能方法。