Question

in triangle ABC if angle A = 100, AD bisects angle A and AD is perpendicular to BC, then angle B is

Answer 1

so easy and simple.............

Answer 2

$In \: \triangle ABC , \angle A = 100\degree$

$and \: AD \:bisects \: \angle A .$

$AD \perp BC$

$\angle A = 100\degree$

$\implies \angle BAD + \angle DAC = 100\degree$

$\implies \angle BAD + \angle BAD = 100\degree$

$\blue { ( AD \:bisects \: \angle A ) }$

$\implies 2\angle BAD = 100\degree$

$\implies \angle BAD = 50\degree$

$In \triangle BAD , \\</p><p>\angle B + \angle {BAD} + \angle {BDA } = 180\degree$

$\pink { ( Angle \:sum \: property ) }$

$\implies \angle B + 50 + 90 = 180\degree$

$\implies \angle B + 140 = 180\degree$

$\implies \angle B = 180\degree - 140 \degree$

$\implies \angle B = 40\degree$

Therefore.,

$\red { Value \:of \: \angle B} \green { = 40\degree }$

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