Question

the angles of a trangle are (10x-5)°,(15x-10)° and (25x-5)°.find their degree measure in a right angled trangle, one of the acute angles is two-thirds of the other.find the angles of the trangle.​

Answer 1

Answer:

1st angle - 35

2nd angle - 50

3rd angle - 95

Step-by-step explanation:

The given angles of a triangle are ;

(10x - 5°) , (15x - 10°) , (25x - 5°) .

Let's take

∠1 = 10x - 5°

∠2 = 15x - 10°

∠3 = 25x - 5°

Also ,

We know that , according to angle sum property of a triangle , the sum of all the three interior angles of a triangle is 180° .

Thus ,

=> ∠1 + ∠2 + ∠3 = 180°

=> (10x - 5°) + (15x - 10°) + (25x - 5°) = 180°

=> 50x - 20° = 180°

=> 50x = 180° + 20°

=> 50x = 200°

=> x = 200°/50

=> x = 4°

Thus ,

∠1 = 10x - 5° = 10•4° - 5° = 40° - 5 = 35°

∠2 = 15x - 10° = 15•4° - 10° = 60° - 10° = 50°

∠3 = 25x - 5° = 25•4° - 5° = 100° - 5° = 95°

Hence ,

The angles of triangle in degrees are ; 35° , 50° and 95° .