Question

help me with the question please

Answer 1

Hi there !

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Given :

3∠A = 4∠B = 6∠C

Solution :

Let 3∠A = 4∠B = 6∠C = x.

Now,

3∠A = x ⇒ ∠A = $\mathsf {\frac {x} {3} }$

4∠B = x⇒ ∠B = $\mathsf {\frac {x} {4} }$

6∠C = x⇒ ∠C = $\mathsf {\frac {x} {6} }$

So,

We know that,

Sum of angles of a triangle is 180 °

∠A + ∠B + ∠C = 180°

$\mathsf{ \frac{x}{3} + \frac{x}{4} + \frac{x}{6} = 180° } \\ \\ \mathsf{ \frac{12x+ 9x + 6x}{36} = 180°} \\ \\ \mathsf {\frac{27x}{36} =180°} \\ \\ \mathsf{27x = 180 \times 36} \\ \\ \mathsf{x = \frac{ \cancel{180} \: {}^{20} \times \cancel{36} \: {}^{12} }{ \cancel{27} \: {}^{ \cancel{ \: 9}} } } \\ \\ \mathsf{x = 20 \times 12} \\ \\ \mathsf{x = 240 }$

Therefore,

∠A = $\mathsf {\frac {x} {3} }$

∠A = $\mathsf {\frac {240} {3} }$

∠A = 80°
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∠B = $\mathsf {\frac {x} {4} }$

∠B = $\mathsf {\frac {240} {4} }$

∠B = 60°
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∠C = $\mathsf {\frac {x} {6} }$

∠C = $\mathsf {\frac {240} {6} }$

∠C = 40°

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Thanks for the question !

☺️❤️☺️

Answer 2

Answer:

∠A = 80º , ∠B = 60º , ∠C = 40º

Step-by-step explanation:

Define x:

Let ∠A be x

Find ∠B in term of x:

3∠A = 4∠B

3x = 4∠B

∠B = 3x/4

Find ∠C in term of x:

4∠B = 6∠C

4(3x/4) = 6∠C

3x = 6∠C

∠C = 3x/6 = x/2

Solve x:

Angles in a triangle add up to 180º

x + 3x/4 + x/2 = 180

9x/4 = 180

x = 180 ÷ 9/4

x = 80

Find each angle:

∠A = x = 80º

∠B = 3x/4 = 3(80)/4 = 60º

∠C = x/2 = 80/2 = 40º

Answer: ∠A = 80º , ∠B = 60º , ∠C = 40º