Question

In a triangle ABC, if 2 anglesA = 3 anglesB = 6 anglesC, calculate anglesA, anglesB and anglesC.​

Answer 1

According to the Question:

2∠A = 3∠B = 6∠C

Equating the first and Third parts of the Equation,

2∠A = 6∠C

Dividing by 2 on both sides,

∠A = 3∠C  → → → [Equation 1]

Equating the Second and Third parts of the Equation,

3∠B = 6∠C

Dividing by 3 on both sides,

∠B = 2∠C   → → → [Equation 2]

Applying Angle Sum Property,

∠A + ∠B + ∠C = 180°

⇒ 3∠C + 2∠C + ∠C = 180°       [∵ From Equation 1 and 2]

⇒ 6∠C = 180°

⇒ ∠C = 180° ÷ 6

∴ ∠C = 30°

Now let's find Angle B and Angle C.

• ∠A = 3∠C

⇒ ∠A = 3 × 30°

∴ ∠A = 90°

• ∠B = 2∠C

⇒ ∠B = 2 × 30°

∴ ∠B = 60°

Know more:

• What is Angle Sum Property?

Angle Sum Property states that sum of all angles in any triangle is always 180°

Answer 2

Given:-

• 2∠A = 3∠B = 6∠C

Find:-

• Measures of ∠A, ∠B and ∠C

Solution:-

F1st we will find the value of both ∠A and ∠B

⇢2∠A = 6∠C..........《Given》

⇢∠A = 6∠C/2

⇢∠A = 3∠C...........➊

Now,

↣3∠B = 6∠C..........〈Given〉

↣∠B = 6∠C/3

↣∠B = 2∠C............➋

we, know that

➩ ∠A + ∠B + ∠C = 180°...........[Angle Sum Property]

where,

• ∠A = 3∠C [Eq. ➊]
• ∠B = 2∠C [Eq. ➋]

✬ Substituting these values:

➩ ∠A + ∠B + ∠C = 180°

➩ 3∠C + 2∠C + ∠C = 180°

➩ 6∠C = 180°

➩ ∠C = 180/6

➩ ∠C = 30°

So, ∠C is equal to 30°

Now, using this value of in ∠C eq. ➊

➨ ∠A = 3∠C

➨ ∠A = 3(30)

➨ ∠A = 90°

So, ∠A is equal to 90°

Now, using value of ∠C in eq. ➋

➤ ∠B = 2∠C

➤ ∠B = 2(30)

➤ ∠B = 60°

So, ∠B is equal to 60°

$\qquad$ ________________________

Hence,

❍∠A = 90°

❍∠B = 60°

❍∠C = 30°