Question : In an isosceles triangle, if the vertex angle is twice the sum of the base angle, then the measure of the half of the vertex angle of the triangle is:
Option 1: 60
Option 2: 70
Option 3: 80
Option 4: 50
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Correct Answer: 60
Solution :
Let the base angle be $x$.
Given, that the vertex angle is twice the sum of base angles.
The sum of base angles = 2$x$
So, vertex angle = 4$x$
We know the sum of angles of a triangle is 180$^\circ$.
So, $x$ + $x$ + 4$x$ = 180$^\circ$
Or, $x$ = 30$^\circ$
Half of vertex angle = 2$x$ = 60$^\circ$
Hence, the correct answer is 60.
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