Question

The base angles of an isosceles triangle is 50 degrees. The size of vertical angle is:
A. $ {55^0} $
B. $ {35^0} $
C. $ {70^0} $
D. $ {80^0} $

Answer 1

Hint: In this question, we need to determine the value of the vertical angle of the isosceles triangle such that the base angles of the triangle has been given as 55 degrees. For this, we will follow the property of the isosceles triangle along with the properties of the general triangles.

Complete step-by-step answer:
According to the question, the base angles of the isosceles triangle are $ {55^0} $ and $ {55^0} $ .
Let the value of the vertical angle of the isosceles triangle be $ {x^0} $ .
The following figure depicts the pictorial data given in the question

Following the property of the isosceles triangles which states that the two sides of the isosceles triangles are same and so the opposite angles associated with those sides will be equal and the vice-versa is also true.
Also, the sum of the interior angles of the triangles will be equal to 180 degrees. Mathematically, $ x + y + z = {180^0} $ where, ‘x’, ‘y’ and ‘z’ are the interior angles of the triangle.
Here, in the question the two interior angles of the isosceles triangle are 55 degrees each. So, substituting the values in the equation $ x + y + z = {180^0} $ to determine the value of the vertical angle.
 $
  x + y + z = {180^0} \\
   \Rightarrow x + 55 + 55 = 180 \\
   \Rightarrow x = 180 - 55 - 55 \\
   \Rightarrow x = 180 - 110 \\
   \Rightarrow x = {70^0} \\
  $
Hence, the vertical angle of the isosceles triangle is 70 degrees.

So, the correct answer is “Option C”.

Note: In an isosceles triangle, the vertical angle is the angle other than the two equal angles (also known as the base angles). Two of the angles of the isosceles triangles are always equal.