Question

Q40. In an isosceles triangle, the
base angles are equal. The
vertex angle is 80°. What are the
base angles of the triangle?
(Remember, the sum of three
angles of a triangle is 180°). *
*​

Answer 1

Answer:

let the base angles be x

x+x+80=180(angle sum property of triangle)

2x=180-80

x=100/2

x=50

therefore each base angle is 50

hope it helps!!

pls mark as the BRAINLIEST!!

Answer 2

» To find :

The Base Angle of the Isosceles triangle.

» Given :

• Vertex angle = 80°.

» We Know :

The sum of the Angles of a Triangle is 180°.i.e,

$\sf{\underline{\boxed{\angle_{1} + \angle_{2} + \angle_{3} = 180^{\circ}}}}$

» Concept :

Let the given Isosceles-triangle be ∆ABC.

So , the vertex $\angle C = 180^{\circ}$

And According to the question , the base Angles are equal , so we can determine them by a single variable , i.e x .

So , according to the given information , the three angles, i.e, $\angle C$ , $\angle A$ and $\angle B$ will sum upto 180°.

So the Equation formed is :

$\sf{\underline{\boxed{\angle A + \angle B + \angle C = 180^{\circ}}}}$

Now , by solving it we will get the other two angles.

» Solution :

• Given Vertex Angle = 80°

Taken , equal base angles is x.

Using the formula ,and Substituting the values in it ,we get :

$\sf{\underline{\boxed{\angle A + \angle B + \angle C = 180^{\circ}}}}$

$\sf{\Rightarrow x + x + 80^{\circ} = 180^{\circ}}$

$\sf{\Rightarrow 2x + 80^{\circ} = 180^{\circ}}$

$\sf{\Rightarrow 2x = 180^{\circ} - 80^{\circ}}$

$\sf{\Rightarrow 2x = 100^{\circ}}$

$\sf{\Rightarrow x = \dfrac{100^{\circ}}{2}}$

$\sf{\Rightarrow x = \dfrac{\cancel{100^{\circ}}}{\cancel{2}}}$

$\sf{\Rightarrow x = 50^{\circ}}$

$\sf{\therefore x = 50^{\circ}}$

Hence ,the other two angles are 50°.

» Additional information :

• Distance Formula :

$\sf{\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}}$

• Properties of Congruency

1. SSS
2. SAS
3. ASA
4. Right angle-hypoteuse Congruency property