Question

One of the base angles of an isosceles triangle is ${70^0}$. The vertical angle is?
$A){60^0}$
$B){80^0}$
$C){40^0}$
$D){35^0}$

Answer 1

Hint: First, we need to know about the isosceles triangle, which is a triangle that has two equal sides in length.
The angles are opposite to the given equal sides of the isosceles triangles, in total ${180^0}$. So, we need to determine the values of the vertical angles of the given isosceles triangle.
Such that the base angle of the triangle has been given as seventy degrees.
We follow the property of the isosceles triangle along with the properties of the general triangle to solve this problem, which is to find the vertical angles.

Complete step by step answer:
According to the base values that are the given isosceles triangle is given as ${70^0}$ (which is one of the bases)
Let the value of the vertical angle of the isosceles is $x$ (unknown).
The following figure depicts the pictorial data of the given question.

One of the bases is ${70^0}$($\angle B$ or $\angle C$) and by the definition of the isosceles triangle two sides of the length are equal and hence we get the other base also ${70^0}$ (If the given base is $\angle C$, then the other base is $\angle B$, similarly for given is $\angle B$, then another base is $\angle C$)
Now we need to find the value of unknown x,
The property of the isosceles triangles which states that the two sides of the isosceles triangles are the same and opposite angles associated with those sides will be equal and vice versa is true.
Hence the sum of the interior angles of the triangle will be equal to ${180^0}$
Express the statement mathematically, we get $\angle A + \angle B + \angle C = {180^0} \Rightarrow {70^0} + {70^0} + x = {180^0}$(the other two angles are given in the question as to the base of ${70^0}$and x is the unknown vertical angle)
To determine the value of x, the vertical angle we solve the further equation, ${70^0} + {70^0} + x = {180^0} \Rightarrow {140^0} + x = {180^0}$
Now equating the angles at one side we get, ${140^0} + x = {180^0} \Rightarrow x = {40^0}$
Hence the vertical angle is ${40^0}$ in the isosceles triangle with the one base ${70^0}$
Hence option $C){40^0}$ is correct.

Note: In the isosceles triangle, the vertical angle is the angle other than the two equal angles (also known as the base angle). The isosceles triangles are always equal in the base angles.
In isosceles triangles, the two bases and one vertical angle are equal to the ${180^0}$.
Since in an isosceles triangle, the sides of two sides are equal. Equilateral triangles are all three sides equal. Scalene triangles are those whose all three sides are unequal.