Question

the angke of a triangke are in the ratio 1:4:5 find angles​

Answer 1

Appropriate Question :

• The Angles of Triangle are in ratio 1:4:5 . Find all angles of Triangle.

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Given : The angles of Triangle is in ratio 1:4:5 .

Need To Find : Measures of all angles of Triangle.

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❍ Let's Consider measure of all three angles of Triangle be 1x, 4x & 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.

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

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 1x + 4x + 5x =\:180\degree}$

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

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

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

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

Therefore,

• First Angle of Triangle is x = 18⁰

• Second angle of Triangle is 4x = 4 × 18 = 72⁰

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

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Measure \:of\:all\:three\:angles \:of\:Triangle \:are\:18\degree, \:72\degree ,\:\:and\:90\degree \: }}}$

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Answer 2

Question :-

• The angles of a triangle are in the ratio 1 : 4 : 5. Find the angles.

Answer :-

• The angles of the triangle are 18°, 72° and 90°.

Given :-.

• The angles of a triangle are in the ratio 1 : 4 : 5.

To find :-.

• The angles of the triangle.

Step-by-step explanation :-

The angles of a triangle are in the ratio 1 : 4 : 5.

So, let the angles be x, 4x and 5x.

We know that :-

$\underline{ \boxed{\sf Sum \: of \: all \: angles \: in \: a \: triangle = 180^{\circ}}}$

So, all these angles must add up to 180°.

$\bf\implies x + 4x + 5x = 180^{\circ}$

Adding x, 4x and 5x,

$\bf\implies 10x = 180^{\circ}$

Transposing 10 from LHS to RHS, changing its sign,

$\bf\implies x = \dfrac{180^{\circ}}{10}$

Dividing 180° by 10,

$\overline{\boxed{\bf \implies x = 18^{\circ}.}}$

• The value of x is 18°.

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Hence, all the angles are as follows :-

$\tt x = 18^{\circ}.$

$\tt4x = 4 \times 18^{\circ} = 72^{\circ}.$

$\tt5x = 5 \times 18^{\circ} = 90^{\circ}.$