Question

If all the angles of the triangle are in ratio of 2:3:5. then find out measurement of all the

angles. Identify the type of triangle.​

Answer 1

Answer:

Step by step explanation:

Ratio = 2 : 3 : 5

Angle sum property of triangle says all angles addition is 180 degree. let the angles be as 2x 3x and 5x

==> 2x + 3x + 5x = 180

==> 10x = 180

==> x = 180/10

==> x = 18

One Angle = 2x = 2 × 18 = 36

Second Angle = 3x = 3 × 18 = 54

Third angle = 5x = 5 × 18 = 90

.°. The angle are 36°, 54° and 90°.

Answer 2

⠀

Given : The angles of Triangle is in ratio 2:3:5 .

Need To Find : Measures of all angles of Triangle.

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❍ Let's Consider measure of all three angles of Triangle be 2x , 3x & 5x .

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

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

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.

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

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 2x + 3x + 5x =\:180\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 5x + 5x =\:180\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 10x =\:180\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ x =\:\dfrac{\cancel {180}}{\cancel {10}}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 18\:\degree}}}}\:\bf{\bigstar}$

Therefore,

• First Angle of Triangle is 2x = 2 × 18 = 36⁰

• Second angle of Triangle is 3x = 3 × 18 = 54⁰

• Third angle of Triangle is 5x = 5 × 18 = 90⁰

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Measure \:of\:all\:three\:angles \:of\:Triangle \:are\:36\degree, \:54\degree ,\:\:and\:90\degree \: }}}$

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C L A S S I F I C A T I O N :

• The one angle of Given Triangle is 90⁰ .

Then ,

• The given Triangle is a Right- Angled Triangle .

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