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Maths-

General

Easy

Question

The angles of a triangle are $left parenthesis x minus 40 right parenthesis to the power of ring operator comma left parenthesis x minus 20 right parenthesis to the power of ring operator text and end text open parentheses x over 2 minus 10 close parentheses$ Find the value of and then the angles of the triangle

hint Hint:

We find the value of x by using the sum of angles in the triangle is 180°.
And substitute value of x to get the angles
Ans :- x = 100°; 60° , 40° and 80° are angles of the triangle .

The correct answer is: Therefore 60° , 40° and 80° are the angles of the triangle.

Step 1:- Find value of x
Let $left parenthesis x minus 40 right parenthesis comma left parenthesis x minus 20 right parenthesis text and end text open parentheses x over 2 minus 10 close parentheses$ are angles of triangles.
$left parenthesis x minus 40 right parenthesis plus left parenthesis x minus 20 right parenthesis plus open parentheses x over 2 minus 10 close parentheses equals 180 to the power of ring operator$
$fraction numerator 5 x over denominator 2 end fraction minus 70 equals 180 not stretchy rightwards double arrow fraction numerator 5 x over denominator 2 end fraction equals 70 plus 180 not stretchy rightwards double arrow x equals 250 open parentheses 2 over 5 close parentheses$
∴x = 100°
Step 2 :-Find the actual angles
$x minus 40 equals 100 minus 40 equals 60 to the power of ring operator$
$x minus 20 equals 100 minus 20 equals 80 to the power of ring operator$
$open parentheses x over 2 minus 10 close parentheses equals 50 minus 10 equals 40 to the power of ring operator$
Therefore 60, 40° and 80° are the angles of the triangle.

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