Question

❤️Math Genius ❤️


the angles of triangle are in ratio of 3:4:5 find the measures of all the angles
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Answer 1

HOLA ______ ^_^

⏩ Sum of all angles of a triangle = 180°

Given angles are in the ratio 3:4:5

3x+4x+5x = 180

12x = 180

x= 180/12

x = 15

SO,

3(15) = 45

4(15) = 60


...✌✌ ...

5(15) = 75

Answer 2

$\textbf{\large{\underline{Answer :-}}}$

$\textbf{\large{\underline{Explaination}}}$

$\textbf{\large{\underline{Given :-}}}$

The Ratio = 3:4:5

$\textbf{\large{\underline{To find :}}}$

The measures of the angles.

$\textbf{\large{\underline{Solution :-}}}$

Consider,

1st Angle = 3x

2nd Angle = 4x

3rd Angle = 5x

As we all know,

The sum of all angles of the triangle is 180°

So,

$\mathsf{\Rightarrow3x + 4x + 5x = 180 }$

$\mathsf{\Rightarrow12x = 180 }$

$\mathsf{\Rightarrow x = \dfrac{180}{12} }$

$\mathsf{\Rightarrow x = 15}$

So,

$\textbf{1st side }$

$\mathsf{\Rightarrow3x }$

$\mathsf{\Rightarrow 3 \times 15}$

$\mathsf{\Rightarrow45\degree }$

$\textbf{2nd side }$

$\mathsf{\Rightarrow 4x}$

$\mathsf{\Rightarrow 15 \times 4}$

$\mathsf{\Rightarrow60\degree }$

$\textbf{3rd side }$

$\mathsf{\Rightarrow5x }$

$\mathsf{\Rightarrow 15 \times 5}$

$\mathsf{\Rightarrow 75\degree}$

$\therefore$The angles are 45°,60° and 75°

$\textbf{\large{\underline{Verification :- }}}$

$\mathsf{\Rightarrow 45 + 60 + 75 = 180}$

$\mathsf{\Rightarrow 180 = 180}$

$\textsf{\large{LHS = RHS}}$

$\therefore$The The angles are 45°,60° and 75°