Question

The sum of two angles of a triangle is 120° and their difference is 20°. The measure of each angle of the triangle is?

Answer 1

Answer:

Solution

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Consider a △ABC,

then according to the given condition we have:

∠A+∠B=80

o

and ∠A−∠B=20

o

⇒2∠A=100

o

⇒∠A=50

o

⇒∠B=30

o

Using the sum of all the angles of the triangle is 180

o

We have: ∠A+∠B+∠C=180

o

⇒50

o

+30

o

+∠C=180

o

⇒∠C=100

o

Hence ∠A=50

o

, ∠B=30

o

and ∠C=100

o

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Answer 2

Step-by-step explanation:

It is given that sum of two triangles is 120°

∠A + ∠B = 120°

And also the difference between them is 20°

∠A - ∠B = 20°

We have to found the measure of each angle of the triangle

Solution:-

∠A + ∠B = 120°

=> ∠A = 120° - ∠B

Substitute the value of ∠A in second equation,

∠A - ∠B = 20°

=> 120° - ∠B - ∠B = 20°

=> 120° - 20° = 2 ∠B

=> 100 = 2 ∠B

=> ∠B = 50°

Substitute the value of ∠B in first equation,

∠A + ∠B = 120°

=> ∠A + 50° = 120°

=> ∠A = 120° - 50°

=> ∠A = 70°

Now we can found the value of other angle by using Angle Sum Property of the triangle,

∠A + ∠B + ∠C = 180°

=> 70° + 50° + ∠C = 180°

=> 120° + ∠C = 180°

=> ∠C = 180° - 120°

=> ∠C = 60°

So,

∠A = 70°

∠B = 50°

∠C = 60°