Question

in a triangle ABC the measure of angle A is 40 degree less than the measure of Angle B and 50 degree less than that of angle C. find the measure of angle A

Answer 1

Answer:

$In \: \triangle ABC,\\\angle A = 30\degree ,\\</p><p>B = 70\degree ,\\C = 80\degree$

Step-by-step explanation:

$In \: \triangle ABC , \\\angle A \:is \: 40\:\degree \:less \:than \\the \: measure \:of \angle B$

$\angle A \:is \: 50\:\degree \:less \:than \\the \: measure \:of \angle C$

$\angle B = \angle A + 40\degree \:---(1)$

$\angle C = \angle A + 50\degree \:---(2)$

$\angle A + \angle B + \angle C = 180\degree$

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

$\angle A + (\angle A+40 )+ (\angle A + 50)=180\degree$

$[ From \:(1)\: and \:(2) ]$

$\implies 3\angle A + 90 = 180$

$\implies \angle A = 180 - 90 = 90$

$\implies \angle A = \frac{90}{3} = 30\degree$

/* Substitute A = 30° in equation (1) and (2) , we get

$\angle B = 30\degree + 40 \degree = 70\degree$

$\angle C = 30\degree + 50 \degree = 80\degree$

Therefore.,

$In \: \triangle ABC,\\\angle A = 30\degree ,\\</p><p>B = 70\degree ,\\C = 80\degree$

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