SOLUTION: In triangle ABC, angle A is twice as large as angle B. Angle B is 4 degrees larger than Angle C. Find the measure of each angle.

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Question 221389: In triangle ABC, angle A is twice as large as angle B. Angle B is 4 degrees larger than Angle C. Find the measure of each angle.
Found 2 solutions by drj, likaaka:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
In triangle ABC, angle A is twice as large as angle B. Angle B is 4 degrees larger than Angle C. Find the measure of each angle.

Step 1. The sum of the angles in a triangle is 180 degrees.

Step 2. Let B=C+4 since Angle B is 4 degrees larger than Angle C.

Step 3. Let A=2B=2(C+4) since Angle A is twice as large as angle B.

Step 4. Then A+B+C=2(C+4)+C+4+C=180

Step 5. Simplifying equation in Step 4 yields the following steps.

2%28C%2B4%29%2BC%2B4%2BC=2C%2B8%2B2C%2B4=180

4C%2B12=180

Subtract 12 from both sides

4C%2B12-12=180-12

4C=168

Divide by 4 to both sides of the equation

4C%2F4=168%2F4

C=42 B=C%2B4=46 and A=2B=2%2A46=92

Check if A+B+C=180 or 42+46+92=180...a true statement.

Step 6. ANSWER: Angle A is 92 degrees, Angle B is 46 degrees and Angle C is 42 degrees.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J

Answer by likaaka(51) About Me  (Show Source):
You can put this solution on YOUR website!
You must set up a system of equations
The interior angles of a triangle always add up to 180°, so A + B + C = 180°
angle A is twice as large as angle B, so A = 2B
angle B is 4° larger than angle C ,so B = C + 4
First begin by solving for A in terms of C
if A = 2B and B = C + 4, then A = 2(C + 4) = 2C + 8
Now we have both angles A & B solved for in terms of C and we substitute them into the first equation
A + B + C = 180
(2C + 8) + (C + 4) + C = 180, the parenthesis are unnecessary here I just used them to show the substitution
Now combine like terms
4C + 12 = 180, subtract 12 from both sides
4C = 168, divide both sides by 4 to solve for C
C = 42, so angle C is 42°
Use C to solve for angles A & B
A = 2C + 8
A = 2(42) + 8
A = 84 + 8
A = 92, so angle A is 92°
B = C + 4
B = 42 + 4
B = 46, so angle B is 46°