Question

The sum of two angles is 115° and their difference is25° find the angles of the triangle​

Answer 1

Answer:

∠A=70 , ∠B=45° and ∠C=65°

Step-by-step explanation:

Let us consider the sum of two angles as ∠A+∠B=115°

and the difference can be written as ∠A−∠B=25°

We know that the sum of all the angles in a triangle is 180°

So we can write it as

∠A+∠B+∠C=180°

By substituting ∠A+∠B=115°

in the above equation

115° + ∠C=180°

On further calculation

∠C=180° − 115°

By subtraction

∠C= 65°

It is given that ∠A−∠B=25°

It can be written as ∠A=25° + ∠B

Now by substituting ∠A=25°+∠Bin∠A+∠B=115°

∠A+∠B=115°

25°+∠B+∠B=115°

On further calculation

25°+2∠B=115°

By subtraction

2∠B=115°−25°

2∠B=90°

By division

$∠B= \frac{90}{2}$

∠B=45°

By substituting ∠B=45° in ∠A=25°+∠B

We get

∠A=25°+45°

By addition

∠A=70

Therefore, ∠A=70 , ∠B=45° and ∠C=65°

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