Math, asked by ravisharma171982, 5 days ago

one angle of a triangle is equal to the sum of the other two 2 if the ratio of the other two angle is 7 : 8 find the angle of triangle​

Answers

Answered by artisonibanda83
3

Step-by-step explanation:

The angles of triangle are 90°, 42° and 48°

Step-by-step explanation:

Given that one angle of a triangle is equal to the sum of other two. if the ratio of the other two angles is 7:8.

we have to find the angles of the

triangle.

Let the angles of triangle be x, y and z

As one angle of a triangle is equal to the sum of other two

x=y+z

also the ratio of the other two angles is

7:8.

y:z=7:8

Let y be 7a and z be 8a

:.x=7a+8a=15a

By angle sum property of triangle

x+y+z=180°

15a+7a+8a=180°

30a=180° → a=6

Hence, angles are

x=15a=15(6)=90°

y=7a=7(6)=42°

please mark it brainliest answer

z=7a=8(6)=48°

Answered by Anonymous
33

Given :-

  • Ratios = 7:8

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To Find :-

  • All the angles = ?

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Need to know :

{\red{\bigstar{\green{\underline{\text{Sum of all angles of a triangle is 180°.}}}}}}

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Solution :-

Let :

{\rightarrowtail{\bf{1st \:  angle = 7x}}}

{\rightarrowtail{\bf{2nd  \: angle = 8x}}}

{\rightarrowtail{\bf{3rd  \: angle = 7x + 8x}}}

{\rightarrowtail{\bf{Sum = 180°}}}

Solving Starts :

{:{\twoheadrightarrow{\sf{7x + 8x + (7x + 8x) = 180°}}}}

{:{\twoheadrightarrow{\sf{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:   \:   \:  \: \: 15x + 15x= 180°}}}}

{:{\twoheadrightarrow{\sf{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:   \:   \:  \: \:  \:  \:  \:   \:  \: \:  \:  \:  \:  \:  \:  \: 30x= 180°}}}}

{:{\twoheadrightarrow{\sf{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:   \:   \:  \: \:  \:  \:  \:   \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: x=  {\cancel\frac{180}{30} }}}}}

{\large{\purple{:{\longmapsto{\underline{\boxed{\bf{X =}{\mathfrak{\red{ \: 6}}}}}}}}}}

Hence :

{\red{➵{\green{\boxed{\sf{1st  \: angle = 7x = 7 \times  6 = 42°}}}}}}

{\red{➵{\green{\boxed{\sf{2nd  \: angle = 8x = 8  \times 6 = 48°}}}}}}

{\red{➵{\green{\boxed{\sf{3rd  \: angle = (7x + 8x) = 15x = 15 6 = 90°}}}}}}</p><p>

For Verification :

{:{\leadsto{\bf{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  Sum  \: of  \: all  \: angles = 180°}}}}

{:{\leadsto{\bf{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 7x + 8x + (7x + 8x) = 180°}}}}

{:{\leadsto{\bf{7 \times  6 + 8 \times  6 + (7  \times 6 + 8 \times  6) = 180°}}}}

{:{\leadsto{\bf{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 42° + 48° + (42° + 48°) = 180°}}}}

{:{\leadsto{\bf{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 90° + 90° = 180°}}}}

{:{\leadsto{\bf{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 180° = 180°}}}}

{\orange{\bf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: {LHS = RHS }}}

Hence, Verified .

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