Question

in adjoining diagram , a rectangle just touches an equilateral triangle . what is the measure of the angle marked x
please tell​

Answer 1

Answer :

x = 50°

Step-by-step explanation :

 Given,

the triangle is an equilateral triangle.

i.e., all the angles are equal.

let each angle of the equilateral triangle be a°

we know that,

sum of the three angles in a triangle = 180°

 a° + a° + a° = 180°

       3a° = 180°

         a =180/3

         a = 60°

Each angle of equilateral triangle = 60°

[ Please refer to the attachment ]

 

we know,

Sum of the angles on a straight line = 180°

     p° + 60° = 180°

      p° = 180° - 60°

       p° = 120°

In ΔABC,

Sum of all the angles = 180°

  20° + p° + q° = 180°

  20° + 120° + q° = 180°

     140° + q° = 180°

       q° = 180° - 140°

        q° = 40°

⇒ The angles in rectangle are 90° each.

   

 Since, the sum of the angles on a straight line = 180°

                 x° + 90° + q° = 180°

                 x° + 90° + 40° = 180°

                x° + 130° = 180°

                 x° = 180° - 130°

                 x° = 50°

       $\boxed{\bf \implies x =50^{\circ}}$