Geometry) If △ABC has angle measures m∠A=(3x)°, m∠B=(x+5)°...

Question

If △ABC has angle measures m∠A=(3x)°, m∠B=(x+5)°, and m∠C=(x−15)°, then ∠__________ has the largest angle measure, which is __________°.

Enter the uppercase letter and number that correctly fill in the blanks from left to right, separated by a comma, like this: N, 42

Answer 1

Klauss,

I would first write an equation to help solve this problem.

The sum of all angles of a triangle is 180 degrees so we can write an equation as follows.

given:m∠A=(3x)°, m∠B=(x+5)°, and m∠C=(x−15)°

3x + (x+5) + (x-15) = 180

3x +x +x +5 - 15 = 180

5x - 10 = 180

5x = 190

x = 38

m∠A=(3x)° = 3(38)^o 114^o

m∠B=(x+5)° = (38+5)^o = 43^o

m∠C=(x−15)° = (38-15)^o = 23^o

Answer: A, 114^o

I hope this helps.

Please feel free to reach me if you still need clarification.

Thanks,

Richmond