Question

The angles of a triangle are in the ratio 1: 3: 2 How much is each angle?​

Answer 1

Answer:

let the angles of the triangle be 1x, 3x and 2x respectively.

= 1x + 2x+ 3x= 180° ( angle sum property)

= 6x= 180°

= x = 180°/6

= x= 30°

= 1x= 1× 30°= 30°

= 3x= 3 ×x = 3× 30° = 90°

= 2x= 2 ×x= 2 × 30° = 60°

It'll surely help you

Answer 2

❍ Let's Consider measure of all four angles of quadrilateral be 1x , 3x , & 2x .

$\frak{\underline { \dag As \: We \:Know \:that \:,}}$

• $\underline {\boxed {\sf{ \star The \:sum\:of \:all\:angles \:of\:Triangle \:is \:180\degree}}}$

Or ,

• $\underline {\boxed {\sf{ \star \angle A + \angle B + \angle C =\:180\degree}}}$

Where ,

• $\angle A , \angle B , \ \& \ \angle C$ are the all three angles of triangle.

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 1x + 3x + 2x =\:180\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 4x + 2x =\:180\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 6x =\:180\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ x =\:\dfrac{\cancel {180}}{\cancel {6}}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 30\:\degree}}}}\:\bf{\bigstar}$

Therefore,

• First Angle of Triangle is x = 30⁰

• Second angle of Triangle is 3x = 3 × 30 = 90⁰

• Third angle of Triangle is 2x = 2 × 30 = 60⁰

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Measure \:of\:all\:three\:angles \:of\:Triangle \:are\:30\degree, \:90\degree ,\: \:and\:60\degree \: }}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\large {\boxed{\sf{\mid{\overline {\underline {\star Verification \::}}}\mid}}}$

$\frak{\underline { \dag As \: We \:Know \:that \:,}}$

• $\underline {\boxed {\sf{ \star The \:sum\:of \:all\:angles \:of\:Triangle \:is \:180\degree}}}$

Or ,

• $\underline {\boxed {\sf{ \star \angle A + \angle B + \angle C =\:180\degree}}}$

Where ,

• $\angle A , \angle B \:and\: \angle C$ are the all three angles of Trianglem.

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 30\degree + 90\degree+ 60\degree =\:180\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 1 20\degree + 60\degree =\:180\degree}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  180\degree = 180\:\degree}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀$\therefore {\underline {\bf{ Hence, \:Verified \:}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀