Question

What will be the value of X??​

Answer 1

Given: Triangle ABC with ang A = 80, ang ABO = 10.

To find: The value of x = ?

Solution:

• Let us consider the point of meeting of lines in the triangle be O.

• Now in triangle AOB, we have:

          ang AOB + ang OBA +ang BAO = 180

          by angle sum property of triangle.

          ang AOB + 10 + 20 = 180

          ang AOB = 50

• Now in triangle ABC,

          AB = BC

          ang B = ang C

          so by angle sum property of a triangle, we get:

          ang A + ang B +ang C = 180

          80 + 2B = 180

         2B = 100

         B = C = 50

• Let ang OCB  = y, so ang ACO = 50 - y.

          ang ABO + ang OBC = ang ABC

          ang OBC = 50 - 10 = 40.

• Now in triangle OCB, by angle sum property of triangle

          angle OCB + ang COB + ang CBO = 180

          y + 360 - 150 - x + 40 = 180

          y - x = -70

          x - y = 70   ............(i)

• in triangle AOC, by angle sum property of triangle

         angle AOC + ang OCA + ang CAO = 180

         x + y - 50 + 60 = 180

         x + y = 170  ................(ii)

• Adding (i) and (ii), we get:

        2x = 240

        x = 120

Answer:

     So the value of x is 120