Answer:
A=84°
B=28°
C=68°
Explanation:
We know the following:
A=3B --> "angle A is three times as large as angle B"
A=C+16 --> "and also 16 degrees larger than angle C"
We can find ∠C by subtracting 16 from both sides from the above statement:
C=A-16
We know that in a triangle there are 180°, therefore we can write the following equation.
A+B+C=180°
1) Substitute 3B as A in the above equation:
3B+B+C=180°
2) Substitute A-16 as C in the above equation:
3B+B+A-16=180°
3) Substitute 3B as A in the above equation:
3B+B+3B-16=180°
4) Combine alike terms:
7B-16=180
5) Add 16 to both sides:
7B=196
6) Divide both sides by 7:
B=28°
Now, lets plug in 28° as B in the first equation we deduced:
A=3B --> A=3(28)
A=84°
Now, lets plug in 84° as A in the second equation we deduced:
A=C+16 --> 84=C+16
C=68°