In triangle ABC, angle A is three times as large as angle B, and also 16 degrees larger than angle C. Find the measure of each angle. (Show how you did it asap)
Accepted Solution
A:
Answer:A=84°B=28°C=68°Step-by-step 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=1805) Add 16 to both sides:7B=1966) 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+16C=68°