Question

The vertical angle of an isosceles triangle is $30°$ more than each of its base angles. find all the angles of the triangle.

Answer 1

Sum of all angles of triangle is $180°$

Let the base angle of an isosceles triangle be $x$.

The vertical angle of an isosceles triangle is $30°$ more than each of its base angles

So, vertical angle $=x+30$.

By angle sum property,

$x+x+x+30=180°$

$3x+30°=180°$

$3x=180°-30°$

$3x=150°$

$x=\frac{150°}{3}$

$x=50°$.

Now, the base angle $=x=50°$

and vertical angle$=x+30$$=50+30=80°$.

Hence, the base angles in an isosceles triangle are $50°,50°$ and the vertical angle is $80°$.