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In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then from the following choices, the angles of the triangle are-

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60 °, 60 °, 60 °

45 °, 45 °, 90 °

50 °, 50 °, 80 °

30 °, 30 °, 120 °

answer is D.

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Detailed Solution

It is given that the vertex angle is

2

times the sum of base angles.
We have to find the angles of the triangles.
Assume the vertex angle be

y

and base angle be

x

of the isosceles triangle.
By the given condition,

y = 2 (x + x)

y = 4 x

......(1)
The sum of the angles in a triangle is

180 °

y + x + x = 180 °

y + 2 x = 180 °

....... (2)
Substitute the value of equation (1) within equation (2),

4 x + 2 x = 180 °

6 x = 180 °

x = 180 ° 6

x = 30 °

The base angle is

30 °

.
Substitute the value of

x

in equation (2),

y = 4 × 30 ° ⇒ y = 120 °

The vertex angle is

120 °

.
Thus the angles are

30 °, 30 °, 120 °

.
Hence option 4 is correct.

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