Question

the angles of a triangle are in the
ratio 1:2:3 find the angles.
​

Answer 1

${\large{\pmb{\sf{\underline{Required solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{About \: Question...}}}}}$

⋆ Correct question: The angles of a triangle are in the ratio 1:2:3 Find the angles.

⋆ Understanding the question: This question says that there is a triangle given whose angles are in the ratio of 1:2:3 Afterwards this question says that we have to find out the angles of triangle. Let us solve this question!

${\bigstar \:{\pmb{\sf{\underline{Given \: that...}}}}}$

⋆ There is a triangle given

⋆ The angles of a triangle are in the ratio of 1:2:3

${\bigstar \:{\pmb{\sf{\underline{To \: find...}}}}}$

⋆ Measurement of all angles of triangle

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

⋆ Measurement of all angles of triangle

• Angle first measure 30°
• Angle second measure 60°
• Angle third measure 90°

${\bigstar \:{\pmb{\sf{\underline{Assumptions...}}}}}$

⋆ Let the common ratio be a

⋆ Let 1a is first angle

⋆ Let 2a is second angle

⋆ Let 3a is third angle

${\bigstar \:{\pmb{\sf{\underline{Knowledge \: required...}}}}}$

⋆ Angle sum property of a triangle says that measure of each angle of a triangle is 180° always i.e., a+b+c = 180°

${\bigstar \:{\pmb{\sf{\underline{Full \: Solution...}}}}}$

~ According to the angle sum property and according to the question,

${\sf{:\implies a+b+c = 180 \degree}}$

${\sf{:\implies 1a+2a+3a = 180 \degree}}$

${\sf{:\implies 3a+3a = 180 \degree}}$

${\sf{:\implies 6a = 180 \degree}}$

${\sf{:\implies a = 180/6}}$

${\sf{:\implies a = 90/3}}$

${\sf{:\implies a = 30}}$

We get common ratio as 30.

~ Now let's carry on

${\pmb{\sf{:\implies Angle \: first \: = 1a}}}$

${\sf{:\implies Angle \: first \: = 1(30)}}$

${\sf{:\implies Angle \: first \: = 30 \degree}}$

${\pmb{\sf{:\implies Angle \: second \: = 2a}}}$

${\sf{:\implies Angle \: second \: = 2(30)}}$

${\sf{:\implies Angle \: second \: = 60 \degree}}$

${\pmb{\sf{:\implies Angle \: third \: = 3a}}}$

${\sf{:\implies Angle \: third \: = 3(30)}}$

${\sf{:\implies Angle \: third \: = 90 \degree}}$