Two angles∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?

[Leo34005]

Two angles∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?

Two angles∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?

A) 102°
B) 2°
C) 78°
D) 90°
E) 180°


If two angles are supplements, their sum is 180 degrees.

Algebraic solution:
measure ∠5 = 78 degrees
measure ∠4 = x (we do not know the measure of this angle yet, so it's x)

So: 78 + x = 180 degrees

^^[because these angles are supplements, we know they have to equal 180 degrees]

If you solve that you find out that x, or measure ∠4, is 102 degrees. Check that by doing 78 + 102 = 180.

Since ∠3 is also supplementary to angle 4, ∠3 = ∠5

Which means ∠3 is 78 degrees.


We have discovered:

Measure ∠4 = 102 degrees
Measure ∠5 = 78 degrees
Measure ∠3 = 78 degrees

Final answer is C) 78°

[tiny-tim]

Hi Leo34005! :smile:

This is very long-winded …

why not just say that, from that definition, there is a unique supplementary angle to any angle (in this case, ∠4), so any two supplementary angles must be equal? :wink: