Supplementary and Complementary Angles:
Two angles are supplementary if they add up to 180°.
Two angles are complementary if they add up to 90°.
For example, if one angle is 70°, its supplement is 180°-70° = 110°
Note the angle and its supplement add 70°+110°=180° as expected.
The complement of the same angle is 90°-70°=20°.
Again, note the angle and its complement add 70°+20°=90° as expected.
Now we are ready to solve the equation.
Let's say the required angle is called x.
The supplement of x is 180-x
The complement of x is 90-x
Twice the complement of x is 2(90 - x)
The problem states that the supplement and twice the complement of the angle differ by 35°, thus:
(180 - x) - 2(90 - x) = 35
Solve the equation to find the value of x.
Operating the parentheses:
180 - x - 180 + 2x = 35
Simplifying:
x = 35
The angle is 35°.