Question

the measures of angle of a triangle are in the ratio 2:3:4. find the measures?
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Answer 1

Answer:

let the common variable for the ratio be 'x'

= 2x 3x 4x

= 2+3+4

= 9x

Answer 2

Given :

The measures of angle of a triangle are in The ratio 2:3:4

➟ Let x be the angles of a triangle are 2x, 3x, 4x .

To find :

➡ The measures=?

solution :

➤ As we know that ,

Sum of the angles in the triangle =180 degree

$\bf \green{ according \: to \: given \: conditions}$

$\implies \large \sf \: 2x + 3x + 4x = 180 \degree \\ \\ \implies \large \sf5x + 4x = 180 \degree \: \\ \\ \implies \large \sf 9x = 180 \degree \: \\ \\ \implies \large \sf \: x = \frac{180 \degree}{9} = 20 \degree \\ \\ \implies \boxed{ \large \sf x = 20 \degree}$

$\implies\large \sf \: then \: angles \: of \: triangle = 2x = 2 \times 20 \degree \: = 40 \degree \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4x = 4 \times 20 \degree = 80 \degree \\ \\ \large \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3x \: = 3 \times 20 \degree = 60 \degree$

➡ This Triangle is acute angled triangle.