Question

In triangle ABC,if angle A+ Angle B =65° angle B+ angle C=140° , find the measure of all angles is the∆

Answer 1

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SOLUTION:

<A + <B + <C = 180° (ASP)
(<A + <B) + <C = 180°
65° + <C = 180°
<C = 180° - 65° = 115°

<B + <C = 140°
= <B + 115° = 140°
= <B = 140° - 115° = 25°

<A + <B = 65°
= <A + 25° = 65°
= <A = 65° - 25° = 40°

Therefore, the angles of the ∆ ABC are:
<A = 40°
<B = 25°
<C = 115°



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Answer 2

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∠A+ ∠B= 65° → 1

∠B+∠C= 140°→2

1  +  2

∠A+ 2∠B+  ∠C = 205° →3

WE KNOW, ∠A+ ∠B + ∠C = 180° →4

SUBTRACT 4 FROM 3

WE GET, ∠B= 25°

THEREFORE

∠A=40°

∠C= 115°