Question

11. Find Exercise 17A The three angles of a triangle measure (2x -10°), (x + 31°) and (5x + 7°). Find the value of x and hence all the angles of the triangle

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Answer 1

Answer:

The value of 'x' is $19^{\circ}$ and the angles of the triangle are $28^{\circ}, 102^{\circ}$ and $50^{\circ}$

Step-by-step explanation:

The given angles of the triangle are (2x -10°), (x + 31°), and (5x + 7°). The question is to find the value of 'x' and hence all the angles of the triangle . We know that a triangle has three sides and three angles. And the sum of the three angles is 180°. Therefore,

    $2x-10^{\circ}+x+31^{\circ}+5x+7^{\circ}=180^{\circ}$

Rearrange the equation to find 'x'

            $8x+28^{\circ}=180^{\circ}$

            $8x=180^{\circ}-28^{\circ}\\\\8x=152^{\circ}\\\\x=\dfrac{152^{\circ}}{8}$

Hence , $x=19^{\circ}$

Therefore the angles of the triangle are given as follows,

  1.    $2x-10^{\circ}=2(19^{\circ})-10^{\circ}$

                 $=38^{\circ}-10^{\circ}$

                 $=28^{\circ}$

   2.    $x+31^{\circ}=19^{\circ}+31^{\circ}$

                   $=50^{\circ}$  

   3.    $5x+7^{\circ}=5(19^{\circ})+7^{\circ}$

                   $=95^{\circ}+7^{\circ}$

                   $=102^{\circ}$  

Hence the value of 'x' is $19^{\circ}$ and the angles of the triangle are $28^{\circ}, 102^{\circ}$ and $50^{\circ}$.