Please solve the 17th problem.
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Q.17. In the following figure; AB is the largest and BC is the smallest side of triangle.
Write the angles x$\xb0$, y$\xb0$ and z$\xb0$ in ascending order of their values.
Dear Student,
Please find below the solution to the asked query:
Here , Exterior$\angle $ BAC + $\angle $ BAC = 180$\xb0$ ( Linear pair angles )
So,
x + $\angle $ BAC = 180$\xb0$ , By substituting value from given diagram
$\angle $ BAC = 180$\xb0$ - x
Similarly we get : $\angle $ ABC = 180$\xb0$ - y and $\angle $ ACB = 180$\xb0$ - z
Then ,
$\angle $ BAC = 180$\xb0$ - x , $\angle $ ABC = 180$\xb0$ - y and $\angle $ ACB = 180$\xb0$ - z --- ( 1 )
i ) Given : AB is largest and BC is smallest side of given triangle , So
AB > AC > BC
And we know theorem : In two unequal sides of triangle , the angle opposite to longer side is larger vice versa .
So ,
$\angle $ ACB > $\angle $ ABC > $\angle $ BAC , Substitute values from equation 1 we get :
180$\xb0$ - z > 180$\xb0$ - y > 180$\xb0$ - x , Now we subtract 180$\xb0$ and get :
- z > - y > - x , Now we multiply by ' - 1 ' and get :
z < y < x ( Ans )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Here , Exterior$\angle $ BAC + $\angle $ BAC = 180$\xb0$ ( Linear pair angles )
So,
x + $\angle $ BAC = 180$\xb0$ , By substituting value from given diagram
$\angle $ BAC = 180$\xb0$ - x
Similarly we get : $\angle $ ABC = 180$\xb0$ - y and $\angle $ ACB = 180$\xb0$ - z
Then ,
$\angle $ BAC = 180$\xb0$ - x , $\angle $ ABC = 180$\xb0$ - y and $\angle $ ACB = 180$\xb0$ - z --- ( 1 )
i ) Given : AB is largest and BC is smallest side of given triangle , So
AB > AC > BC
And we know theorem : In two unequal sides of triangle , the angle opposite to longer side is larger vice versa .
So ,
$\angle $ ACB > $\angle $ ABC > $\angle $ BAC , Substitute values from equation 1 we get :
180$\xb0$ - z > 180$\xb0$ - y > 180$\xb0$ - x , Now we subtract 180$\xb0$ and get :
- z > - y > - x , Now we multiply by ' - 1 ' and get :
z < y < x ( Ans )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards