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General
Easy

Question

The measures of the angles of a triangle are 2 square root of 2 x end root comma square root of 2 x end root text   and   end text 6 square root of 2 x end root.
Find the measure of each angle and classify the triangle by its angles.

hintHint:

Find the value of x by using the sum of angles in a triangle is 180° . Now, find values of  all angles .

The correct answer is: x = 200 , angles of the triangle as 40° , 20° and 120°.


    ANS :- x = 200 , angles of the triangle as 40°, 20° and 120°.
    Explanation :-
    Step 1:- Find the value of x
    The angles of triangle are 2 square root of 2 x end root comma space square root of 2 x end root text  and  end text 6 square root of 2 x end root
    2 square root of 2 x end root plus square root of 2 x end root plus 6 square root of 2 x end root = 180°
    9 square root of 2 x end root equals 180
    square root of 2 x end root equals 20 not stretchy rightwards double arrow 2 x equals 400
    ∴ X = 200
    Step 2:- Find the value of angles
    The angles of triangle are = 2 × 20 = 40°
    square root of 2 x end root = 20 = 20°
    6 square root of 2 x end root = 6 × 20 = 120°
    We get angles of the triangle as 40°, 20° and 120° .
    As 120° (> 90°) is an obtuse angle .
    Then the given triangle will be an obtuse angled triangle

     

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