Question

If < A and < B are supplementary, and < A = 3x - 5 degrees, and < B = x + 11 degrees, find x.

Answer 1

Given:

`\begin{gathered} \angle A=3x-5\text{ degre}es \\ \angle B=x+11\text{ degr}ees \end{gathered}`

Supplementary angles are two angles whose measures add up to 180°.

Hence, since angles A and B are supplementary, they add up to 180 degrees.

`\begin{gathered} \angle A+\angle B=180^0 \\ (3x-5)+(x+11)=180^0 \\ C\text{ ollecting like terms;} \\ 3x+x-5+11=180 \\ 4x+6=180 \\ 4x=180-6 \\ 4x=174 \\ \text{Dividing both sides by 4 to solve for x,} \\ x=(174)/(4) \\ x=43.5^0 \end{gathered}`

Therefore, x is 43.5 degrees.