Question

If in a traingle ABC first angle is twice of the second angle and third angle is thrice of the first one. find the measure of each angle of the traingle.​

Answer 1

Given :-  

In a triangle ::

• first angle is twice of the second angle  

• third angle is thrice of the first one

To Find :-  

• All the angles of a triangle  

Solution :-  

⇒ Here , we’re given the information regarding the angles of a triangle and we can find all the angles by the angle sum property of triangle  

• ∠A = First angle  
• ∠B = Second angle
• ∠C = Third angle  

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According to the Question ::  

∠A = 2∠B  

∠B = ∠B  

∠C = 3(2∠B) = 6∠B  

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As we know that ,  

• Sum of all angles of a triangle is 180 according to the angle sum property of a triangle  

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The angles of the triangle can be written as :-  

→ ∠A + ∠B + ∠C = 180°  

→ 2∠B + ∠B + 6∠B = 180°

→ 9∠B = 180°  

→ ∠B = 180°/9  

→ ∠B = 20°

→ ∠A = 40°  

→ ∠C = 120°  

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Therefore,  

Angles of the triangle are 20° ,40° and 120°

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Answer 2

Given

• In a ΔABC
• First angle = Twice the second angle
• Third angle = Thrice the first angle

To find

• All the angles of the triangle

Solution

⇨ Let the angles of the triangle be :-

1. ∠A
2. ∠B
3. ∠C

⇨ Now, according to the question :-

• ∠A = 2∠B
• ∠B = ∠B
• ∠C = 3∠A
• ∠C = 3(2∠B)
• ∠C = 6∠B

⇨ We know that, sum of all the angles in a triangle = 180°

                     (Angle sum property)

⇨ Adding up all the angles, we get :-

• ∠A +  ∠B +  ∠C = 180°
• 2∠B + ∠B + 6∠B  = 180°
• 9∠B = 180°
• ∠B = 180/9
• ∠B = 20°

Now let's substitute the value of ∠B and find the remaining angles :-

• ∠A = 2∠B
• ∠A = 2(20)
• ∠A = 40°

⇨ Measure of ∠A = 40°

• ∠C = 6∠B
• ∠C = 6(20)
• ∠C = 120°

⇨ Measure of ∠C = 120°

Verification

• ∠A + ∠B + ∠C = 180°
• 20°  + 40°  + 120°  = 180°
• 180° = 180°
• L.H.S = R.H.S