Question

In the figure below, ABC is a right triangle. a+b= 150 degrees, and c+d= 35 degrees. Find x.

Answer 1

Alright, lets get started.

These two triangles ABC and ACD are jointly forming a polygon having 4 sides ABCD.

The sum of all internal angles of a polygon having 4 sides = 360

∠A + ∠B + ∠C + ∠D = 360

Plugging the values of each angle

$(a+b) + 90 + (c+d) + x = 360$

$150 + 90 + 35 + x = 360$

$275 + x = 360$

Subtracting 275 from both sides

$275 + x - 275 = 360 - 275$

$x = 85$°

Hence the option is C. (85) : Answer

Hope it will help :)

Answer 2

The answer is C. if you do some simple geometry you find that d is no more than 5 degrees, and it's just subtracting and adding from there