Question

a,b,c are the three angles of a triangle abc if a-b=15,b-c=30,find the angles

Answer 1

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Answer 2

$\angle A , \angle B \:and \: \angle C \: are \\three \: angles \: of \: a \: triangle ABC .$

$\angle A - \angle B = 15\degree \\</p><p>\implies \angle A = 15 \degree + \angle B \: --(1)$

$\angle B - \angle C = 30\degree \\</p><p>\implies \angle C = \angle B - 30\degree \: --(2)$

$\blue { (By \: Angle \: Sum \: Property )}$

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

/* Substitute (1) and (2) in equation (3), we get */

$\implies 15 \degree + \angle B + \angle B +\angle B - 30\degree = 180\degree$

$\implies 3\angle B - 15\degree = 180\degree$

$\implies 3\angle B = 180 \degree + 15\degree$

$\implies 3\angle B = 195 \degree$

$\implies \angle B = \frac{195 \degree}{3}$

$\implies \angle B = 65 \degree$

/* Put <B = 65° in equations (1) and (2), we get */

$\implies \angle A = 15 \degree +65\degree$

$\implies \angle A = 80 \degree$

$And \: \angle C = 65 \degree - 30\degree$

$\implies \angle C = 35\degree$

Therefore.,

$\green { \angle A = 80\degree, \: \angle B = 65\degree \: and \: \angle C = 35\degree}$

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