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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

ABC is a tria...

Question

ABC is a triangle in which $∠ A = 72^{o},$ the internal bisectors of angles Band C meet in O. Find the magnitude of $∠ B O C$ .

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Solution

$∠ A = 72^{\circ}$
By angle sum property
$∠ A + ∠ B + ∠ C = 180 ∠ B + ∠ C = 180 - 72 = 108 ∠ O B C + ∠ O C B = 54$
The Angular bisectors Meet at $O$
So By Angle sum property ,
$∠ O B C + ∠ O C B + ∠ B O C = 180 54 + ∠ B O C = 180 - 54 ∠ B O C = 126$

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