Question

The angle of a triangle are in the ratio 3 ratio 5 ratio 7 find the measures of these angles

Answer 1

Answer:

We know that,

Let the unknown value be k.

Sum of all interior angles of a triangle is 180°.

∴3k+5k+7k=180°

⇒15k=180°

∴k=180÷15

k=12°

⇒3k=3×12°

       =36°

⇒5k=5×12°

      =60°

⇒7k=7×12°

      =84°

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

${\underline{\sf{\blue{Given :}}}}$

Angles of Triangle are in ratio 3:5:7

$\rule{200}{1}$

${\underline{\sf{\green{Solution :}}}}$

Let the angles be 3x, 5x, 7x

So,

$\large \star {\boxed{\sf{180^{\circ} \: = \: Sum \: of \: angles \: of \: Triangle }}}$

Due to angle sum property of triangle

$\implies {\sf{180 \: = \: 3x \: + \: 5x \: + \: 7x}}$

$\implies {\sf{180 \: = \: 8x \: + \: 7x}}$

$\implies {\sf{180 \: = \: 15x}}$

$\implies {\sf{x \: = \: \dfrac{\cancel{180}}{\cancel{15}}}}$

$\implies {\sf{x \: = \: 12}}$

$\rule{200}{1}$

Angles are :

• 3x = 3(12) = 36°

• 5x = 5(12) = 60°

• 7x = 7(12) = 84°