Question

in triangle ABC angle A- angle B=42° and angle B-angle C=21° then what would be the angle B​

Answer 1

Answer:117°

Step-by-step explanation:

Angle sum of a triangle - 180°

angle A + angle B + angle C = 180°

42°+ angle B + 21°= 180°

Angle B = 180°-63°

= 117°

Answer 2

Answer:

Step-by-step explanation:

It is given that,

$Angle\ A - Angle\ B = 42\° -------(1) \\\\Angle\ B - Angle\ C = 21\° ------- (2)$

As we know that the sum of interior angles of a triangle is 180°.

So,

$Angle\ A+Angle\ B+Angle\ C=180\° ----- (3)$

By adding equation (1) and (2),

$Angle\ A- Angle\ B+ Angle\ B- Angle\ C= 42\°+ 21\°\\\\Angle\ A- Angle\ C= 63\° -----(4)$

By subtracting equation (4) from equation (3),

$(Angle\ A+ Angle\ B+ Angle\ C) - (Angle\ A+Angle\ C) = 180\°- 63\°\\\\Angle\ A+ Angle\ B+ Angle\ C- Angle\ A- Angle\ C= 117\° ----(5)$

By multiplying 2 in equation (2) we get,

$2 (Angle\ B- Angle\ C) = 2 * 21\°\\\\2 Angle\ B- 2 Angle\ C= 42\° ------(6)$

Now by adding equation (5) and (6) we get,

$Angle\ B+ 2 Angle\ C+ 2 Angle\ B- 2 Angle\ C= 117\°+42\°$

$3 Angle\ B= 159\°\\\\Angle\ B= 159\°/3\\\\Angle\ B= 53\°$

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