Question

iv. The three angles of a triangle are in the ratio 1:2:3. Find the measure of each
angle.
​

Answer 1

Ratio of the angles = 1:2:3

Total parts = 1 + 2 + 3 = 6

180/6 = 30°

1st part = 1 × 30 = 30°

2nd part = 2 × 30 = 60°

3rd part = 3 × 30 = 90°

Answer 2

⠀

Given : The angles of Triangle is in ratio 1:2:3 .

Need To Find : Measures of all angles of Triangle.

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

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

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

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.

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

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

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

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

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

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

Therefore,

• First Angle of Triangle is x = 30⁰

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

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

Therefore,

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

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V E R I F I C A T I O N :

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

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

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.

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

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

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

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

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

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