Name: Naming Triangles Based on Their Sides
Uploaded: 2019-07-19
Duration: 7 min 40 s
Description: We all have names that we are identified with. Triangles also have such names to help classify them based on their sides. Know about all these types of trian...

Question

In a triangle

A B C

, if

3 ∠ A = 4 ∠ B = 6 ∠ C

, find the angles.

Accepted Answer

Given, $\begin{array}{l} 3 ∠ A = 4 ∠ B = 6 ∠ C \end{array}$

$\begin{array}{l} \Rightarrow ∠ B = \frac{3 ∠ A}{4} \end{array}$ and $∠ C = \frac{3 ∠ A}{6} = \frac{∠ A}{2}$ ....(i)

We know that,
Sum of all interior angle of a triangle is $180 °$

$\begin{array}{l} \Rightarrow ∠ A + ∠ B + ∠ C = 180 ° \end{array}$

$\begin{array}{l} \Rightarrow ∠ A + \frac{3 ∠ A}{4} + \frac{∠ A}{2} = 180 ° \end{array}$

$\begin{array}{l} \Rightarrow \frac{4 ∠ A + 3 ∠ A + 2 ∠ A}{4} = 180 ° \end{array}$

$\begin{array}{l} \Rightarrow \frac{9 ∠ A}{4} = 180 ° \end{array}$

$\begin{array}{l} \Rightarrow 9 ∠ A = 180 ° \times 4 \end{array}$

$\Rightarrow ∠ A = \frac{180 ° \times 4}{9} = 80 °$

$\Rightarrow ∠ B = \frac{3 ∠ A}{4} = \frac{3 \times 80 °}{4} = 60 °$

$\Rightarrow ∠ C = \frac{∠ A}{2} = \frac{80 °}{2} = 40 °$

Hence, the required angles are $80 °, 60 °$ and $40 °$ .

In a triangle $A B C$ , if $3 ∠ A = 4 ∠ B = 6 ∠ C$ , find the angles.

Important Questions on Triangles

Learn and Prepare for any exam you want !

In a triangle ABC, if 3∠A=4∠B=6∠C, find the angles.

Important Questions on Triangles

Learn and Prepare for any exam you want !

In a triangle $A B C$ , if $3 ∠ A = 4 ∠ B = 6 ∠ C$ , find the angles.