Question

the angles of a triangle are in the ratio 1:4:7. find their measures.​

Answer 1

Step-by-step explanation:

let the angle be x,

sum of all angles of triangle is always 180°,

then, x+4x+7x=180°

x+4x+7x=180°

12x =180°

x= 180°/12

x= 15°

it means, 4x=4*15

=60°

7x=7*15

=105°

Answer 2

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• Angles of the triangle are in ratio 1:4:7.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• All angles of the triangle.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Angle Sum Property :-

Sum of all interior angles of a triangle is 180°.

________________

Let the angles be x , 4x and 7x as ratio is 1:4:7.

→ x + 4x + 7x = 180

→ 12x = 180

→ x = 180/12

→ x = 15

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Angles are :-

• x = 15°

• 4x = 4(15) = 60°

• 7x = 7(15) = 105°

Hence , angles are 15° , 60° and 105°.

$\\ \\ \large\underline{ \underline{ \sf{ \red{verification:} }}}$

Sum of these angles should be 180°

15 + 60 + 105 = 180

180 = 180 ㅤㅤㅤㅤㅤㅤㅤ(verified)