in a triangle, angle b is the 12 degrees larger the angle A. angle C is equal to the sum of the first two angles. find the angles

Question

in a triangle, angle b is the 12 degrees larger the angle A. angle C is equal to the sum of the first two angles. find the angles

Answer 1

B=12 + A   AND C=A + B.  Since it is a triangle, A + B + C = 180 degrees.  You can now substitute (12 + A) in for B and solve an equation for C in terms of A.

 

C = A + (12 + A),     C= 2A + 12

 

At this point, you can input the equations for B and C in terms of A into the last equation A + B + C = 180.

A + (12 + A) + (2A + 12) = 180   Now collect like terms.

4A + 24 = 180      Use Order of operations to solve for A. In this case, subtract first.

4A = 156    Divide.

A = 39    Use A to solve for B and C.

B = 12 + A = 12 +39 = 51

C = 2A + 12 =  2(39) + 12 = 78 + 12 = 90

 

If our work was done correctly, A + B + C = 180

A = 39, B = 51, C = 90

39 + 51 + 90 = 180     The answer checks out!

Hope this helps.

Answer 2

b = a+12,  c = a+b = a+(a+12) = 2a+12,

 

a+b+c=180

a+(a+12)+(2a+12)=180

4a+24=180, solve for a, then b and c