Q. 44.5( 11 Votes )
Given: Our given triangle is isosceles triangle. Also, the vertex angle is twice the sum of the base angles
To find: Measures of angles of triangle.
It is given that that given triangle is isosceles triangle.
Let vertex angle be y and base angles be x each.
So by given condition,
y = 2(x + x)
∴ y = 4x
Also, We know that,
Sum of all angles in any triangle = 180°
∴ y + x + x = 180°
y +2x = 180°
4x + 2x = 180°
∴ 6x = 180°
x = 30°
∴ y = 4 × 30°
y = 120°
Hence, vertex angle is 120° and base angles are 30° each.
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