Question

EXAMPLE 3 Two supplementary angles differ by 34º. Find the angles.
SOLUTION Let one angle be r°. Then, the other angle is (x + 34).
It is given that x° and (x +34) are supplementary angles.
please tell me that why

we are adding (X+34), the question is saying that "differ by 34°" so can't we say the another angle will be( x-34)? need the reason why we are adding 34 here ? ​

Answer 1

Answer:

1 supplementary angle (r°) will be equal to 180°

The other angle will be equal to ( x + 34 ) = 180

(Since the problem states that the angle differs by 34°)

Because the problem states that it differs by 34°, that is the same thing as 180 - 34 = 146

146 is equal to 'x' in the equation ( x + 34 ).

If we check our solution, 146 + 34 = 180 ✔️

A supplementary angle is NOT equal to 112, that is why the equation cannot be ( x - 34 ).

( If we input 146 for the variable 'x' : 146 - 34 is equal to 112, not 180°

Hope this helps!