The second angle of a triangle is 45° more than the smallest angle. The third angle is three times the smallest. How many degrees are there in each angle?
Answers
☞Understanding the Question :
The Question says that the second angle of the triangle is 45° more than the smallest angle.And the third angle of the triangle is three times the smallest angle of the triangle.Then we have to find the angles of the triangle.
✶ Let's Solve !
•Firstly let's consider the smallest angle as x
∴ First angle = x
•Then it is given that the second angle of the triangle is more than the smallest angle,
∴ Second angle = x + 45°
•And the third angle of the triangle is 3 times the smallest angle,
∴ Third angle = 3(x) = 3x
→Now,Main Solution :
It is well known that the ,
❃Sum of all angles of a triangle = 180°
Thus,
⇉x + x + 45 + 3x = 180°
⇉x + x + 3x = 180° - 45
⇉5x = 135°
⇉x = 135/5
⇉x = 27°
⇢Thus,the first angle of the triangle is 27°
Likely,
⇢The second angle = x + 45 = 27 + 45 = 72°
⇢And the third angle = 3x = 3 × 27 = 81°
______________________________
★For more satisfaction of our answer, let's verify it !
So,For the sum of all the three angles the sum should be 180°
⇝27° + 72° + 81° = 180°
⇝99° + 81° = 180°
⇝180° = 180°
Thus,the angles we found are correct.
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