Question

The angles of a triangle are in the ratio 1:2:3. The measure of the
largest angle is​

Answer 1

Given:

• Ratio = 1:2:3
• Angles of Triangles = 180°

To Find

• All angles Measurements?
• The Measure of Largest Angle?

Solution:

We Know that,

Sum of all the angles of the Triangle is 180°.

$\\ \circ \: {\boxed{\tt\large\gray{ Total \ Sum \ of \ Angles_{( \Delta )} = 180° }}}$

Let the angle be x

According to Question,

As we know sum of Triangles,

$\colon\implies{\tt{ x + 2x+3x = 180° }} \\ \\ \\ \colon\implies{\tt{ 6x = 180° }} \\ \\ \\ \colon\implies{\tt{ x = \dfrac{ \cancel{180} }{ \cancel{6} } }} \\ \\ \\ \colon\implies{\boxed{\tt\red{ x = 30° }}}$

After Putting values,

$\colon{\boxed{\boxed{\tt\green{ x = 30° }}}}$

$\colon{\boxed{\boxed{\tt\blue{ 2x = 2 \times 30 = 60° }}}}$

$\colon{\boxed{\boxed{\tt\pink{ 3x = 3 \times 30 = 90° }}}}$

Hence,

• The measure of the Largest Angle is 90° .

Answer 2

Answer:

★ Given

• ${\mapsto\textsf{Angles of a triangle are in the ratio - 1:2:3}}$

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ To Find

• $\mapsto \textsf{Measurement of all angles }$
• $\mapsto \textsf{The largest angle of Triangle }$

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ Solution

✒ We know that the sum of all angles of the triangle is 180⁰.

✒ Let the angles be 'x'

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

So,

Angles

• $\leadsto \tt \purple{1 × x} = \pink{1x}$
• $\leadsto \tt \purple{2 × x }= \pink {2 x}$
• $\leadsto \tt \purple{ 3 × x }= \pink {3x}$

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Now,

$\implies\sf \pink{1x + 2x + 3x }= \purple {180 \degree} \\ \\ \implies \sf \pink{6x} = \purple{180 \degree} \\ \\ \implies \sf \pink{x }= \purple{\cancel\dfrac{180}{6} } \\ \\ \implies \sf \pink{x }= \purple{30 \degree} \\ \\ \Large{\underline{\boxed{\frak \pink{x}= \purple{30\degree}}}}$

The Value of x is 30⁰.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Angles

✒ After putting value of x.

• $\leadsto \tt \purple{1 \times 30\degree }= \pink{30\degree}$
• $\leadsto \tt \purple{2 \times 30 \degree }= \pink{60\degree}$
• $\leadsto \tt \purple{3 \times 30 \degree }= \pink{90\degree}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ Therefore

✒ The angles are 30⁰,60⁰ and 90⁰.

✒ And the largest angle is 90⁰.

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ Verification Also :-

The sum of all angles of a triangle is 180⁰

So,

$\implies\sf \pink{30 \degree + 60 \degree + 90 \degree} = \purple{180 \degree} \\ \\ \implies\sf \pink{180 \degree} = \purple{180 \degree} \\ \\ \implies\large{\underline{\boxed {\sf \pink{LHS} = \purple{RHS }}}}$

Hence Verified ✔