In ∆abc the angle bisectors drawn from vertices a and b intersect at point d. find ∠adb if:
m∠с = γ

∠ADB = 90°+0.5γ

Step-by-step explanation:

Given that;

∠ADB =180°-(1/2 ∠A + 1/2 ∠B)sum of interior angles of the triangle ABD add upto 180°

From the other side;

∠A + ∠B + ∠C =180° (i)

Equation (i) is equal to 1/2 ∠A + 1/2 ∠B = 90°-1/2∠C thus

∠ADB = 180°-(1/2 ∠A + 1/2 ∠B) = 180°-(90°-1/2∠C) = 90°+1/2∠C

So in terms of γ where ∠C=γ

∠ADB = 90° + 1/2 γ

∠ADB = 90° + 0.5γ

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

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