Find the value of x.

  155°

Step-by-step explanation:

The obtuse angle of the large (outside) triangle is the supplement of 60°, so is ...

  180° -60° = 120°

The angle x is the sum of the remote interior angles of that large triangle:

  x = 35° +120° = 155°

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Check

The other acute angle in the smaller (left) right triangle is 90° -35° = 55°. Then the top acute angle in the larger (bottom, right) right triangle is ...

  180° -55° -60° = 65°

The other acute angle in that triangle is 90° -65° = 25°. It is supplementary to angle x. Hence angle x is 180° -25° = 155°, as above. (Note that x is also the sum of 90° and 65°, the remote interior angles of the nearest right triangle to x.)