Question

In an isosceles triangle, if the third angle is greater than or equal to ${80}^{\circ }$ then the maximum value each base angle can have is

• A. ${100}^{\circ }$
• B. ${50}^{\circ }$
• C. ${40}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is B ${50}^{\circ }$

Since our triangle is an isosceles triangle, its base angles will be equal.
Let each base angle of the triangle be $x^{\circ }$.
To acsertain the maximum value for $x$ we should know the minimum value of the third angle.
The minimum value for the third angle is ${80}^{\circ }$.(Given)
So using the angle sum propery:
$80+x+x=180$
$80+2x=180$
$2x=180-80$
$2x=100$
$x={50}^{\circ }$