Question

The angles of a triangle are in ratio 1 : 3 : 5. Find the measure of each of the angles.​

Answer 1

Step-by-step explanation:

Letanglesoftrianglebex,3xand5x

Asweknowthat

⇒Sumofallanglesoftriangle=180

∘

⇒∴x+3x+5x=180

∘

⇒9x=180

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x=20

∘

,3x=60

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and5x=100

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Ans.

Answer 2

★ How to do :-

Here, we are given with the ratio of three sides of a triangle. We are asked to find the value of all the sides of the triangle by using the information given. So, we can solve this question by using some other concepts of maths. These concepts are transportation of numericals from LHS to RHS and also the concept of variables. These two concepts are very useful in these type of problems. If we know the formulas of the triangle, then we can solve any problem related to triangle. We should know that all the angles of any triangle measures 180° together. If not, then it's not considered as a triangle.

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➤ Solution :-

${\tt \leadsto 1:3:5 = {180}^{\circ}}$

${\tt \leadsto 1x + 3x + 5x = {180}^{\circ}}$

${\tt \leadsto 9x = {180}^{\circ}}$

${\tt \leadsto x = \dfrac{180}{9}}$

${\tt \leadsto x = {20}^{\circ}}$

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Now,

Measurement of ∠1 :-

${\tt \leadsto 1x = 1 \times 20}$

${\tt \leadsto \angle{1} = {20}^{\circ}}$

Measurement of ∠2 :-

${\tt \leadsto 3x = 3 \times 20}$

${\tt \leadsto \angle{2} = {60}^{\circ}}$

Measurement of ∠3 :-

${\tt \leadsto 5x = 5 \times 20}$

${\tt \leadsto \angle{3} = {100}^{\circ}}$

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Verification :-

We know that all the angles of the triangle together measures 180°. So,

${\tt \leadsto 1:3:5 = {180}^{\circ}}$

${\tt \leadsto 20 + 60 + 100 = 180}$

${\tt \leadsto 180 = 180}$

Hence verified !!