Originally Posted by
chellyluv In triangle ABC, the complement to angle A measures 38 degrees 49 minutes 48 seconds and the supplement to angle B measurres 76 degrees 23 second. What is the measure of angle C?
Hi chellyluv,
You need only find the measure of angle A.
Since you know the supplement of angle C,
you can use the exterior angle theorem of a triangle to find C.
The measure of an exterior angle of a triangle
is equal to the sum of the measures of the two remote interior angles.
Find the measure of angle A:
Code:
90 00' 00" 89 59' 60"
- 38 49' 48" - 38 49' 48"
----------- -----------
51 10' 12"
Now, since the supplement of angle B
is equal to the sum of the measures of angles A and C,
we can subtract the measure of angle A from that of B's supplement,
and we've found angle C.
Code:
76 00' 23" 75 60' 23"
-51 10' 12" - 51 10' 12"
----------- -----------
24 50' 11"