Question

The angles of a triangle are in the ratio

5:3:7.Find each angles of a triangle using angle sum property of triangle.​

Answer 1

Answer:

The angles of the triangle are in the ratio: 5:3:7

Let the angles be 5x,3x,7x

By Angle sum property,

5x+3x+7x=180

15x=180

x=12

Thus, angles are, 60

∘

,36

∘

,84

∘

Since, all the angles are less than 90

∘

, it is an acute angled triangle.

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Answer 2

Given :-

• Angles of triangle in ratio of = 5 : 3 : 7
• Also Angle sum property of triangle.

To find :-

• Each angles of triangle

Concept :-

• Here concept of angle sum property will be used.
• Angle sum property :- It states that sum of all interior angle is 180°. It means that total measure of all three angles is 180°.

Assumption :-

• Let ratio be x form such that they could be added to get the value of x. as
• 5x, 3x, 7x

Solution :-

Making an equation

${ \longmapsto{ \mathtt{5x + 3x + 7x = 180 \degree}}}$

Further solving it :-

${ \longmapsto{ \mathtt{15x = 180 \degree}}}$

${ \longmapsto{ \mathtt{x = \dfrac{ 180 \degree}{15}}}}$

${ \boxed{ \longmapsto{ \mathtt{x = 12 \degree}}}}$

Here all angles are :-

(1) Angle 1

$\large{ \implies{ \mathtt{5x =5 \times 12 }}} \\ \large{ \underline{ \boxed{ \pink{ \implies{ \mathtt{60\degree}}}}}}$

(2) Angle 2

$\large{ \implies{ \mathtt{3x=3\times 12 }}} \\ \large{ \underline{ \boxed{ \pink{ \implies{ \mathtt{36\degree}}}}}}$

(2) Angle 3

$\large{ \implies{ \mathtt{7x =7\times 12 }}} \\ \large{ \underline{ \boxed{ \pink{ \implies{ \mathtt{84\degree}}}}}}$

$\rule{200}{2}$

VERIFICATION :-

=》60° + 36° + 84° = 180°

=》96° + 84° = 180°

=》180° = 180°

Here LHS = RHS

Hence our all answers are correct.

$\rule{200}{2}$

It is a Scalene Triangle.