Question

The angles of a triangle are in AP and the biggest angle is 60.Find the other two

Answer 1

Answer:

Step-by-step explanation:Let a - d, a, a + d be the three angles of the triangle that form AP.

Given that the greatest angle is twice the least.

Now, 2(a - d) = a + d

2a - 2d = a + d

a = 3d ---------------(1)

Now by angle sum property,

(a - d) + a + (a + d) = 180°

3a = 180°

a = 60°----------------------(2)

from (1) and (2),

3d = 60°

d = 20°

Now, the angles are,

a - d = 60°- 20° = 40°

a = 60°

a + d = 60° + 20° = 80°

Answer 2

$let \: the \: angles \: be \: a - d \: and \: a \: nd \: a + d \\ we \: know \: that \: largest \: angle \: is \: 60 \\ so \: 60 = a + d \: \\ in \: the \: triangle \: sum \: of \: angles \: is \: 180 \\ a + d + a + a - d = 180 \\ 3a = 180 \\ a = 60 \\ and \: a + d = 60 \\ d = 0 \\ so \: remaining \: angles \: are \: 60and \: 60$

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