Definition of Complementary Angles

$$\angle A$$ and $$\angle C$$ are both complementary to $$\angle B$$. If $$m\angle A = (6x+7)^{\circ}$$ and $$m\angle C = (8x-13)^{\circ}$$, what is $$m\angle B$$?

Correct! Two angles are complementary if their measures add up to 90°. Therefore, if $$\angle A$$ is complementary to $$\angle B$$, and $$\angle C$$ is complementary to $$\angle B$$, then $$\angle A$$ and $$\angle C$$ must have equal measures. $$\displaystyle m\angle A = m\angle C$$ $$\displaystyle 6x+7=8x-13$$ $$\displaystyle 7=2x-13$$ $$\displaystyle 20=2x$$ $$\displaystyle 10=x$$ Now that you know what the value of _x_ is, you are able to use substitution to find the measure of either $$\angle A$$ or $$\angle C$$. $$\displaystyle m\angle A = 6x+7 = 6(10)+7=60+7 = 67^{\circ}$$ $$\displaystyle m\angle C = 8x-13=8(10)-13 =80-13=67^{\circ}$$ To find $$m\angle B$$, subtract 67 from 90. Therefore, $$m\angle B = 23^{\circ}$$.

Incorrect. [[snippet]] Be sure you are answering the question; 10º is an answer you find during the process, but it is not the answer to the question.

Incorrect. [[snippet]] Be sure you made the correct calculations. There are multiple steps to find a solution, and one small error can lead to an incorrect final solution.

Incorrect. [[snippet]] While 67º is an answer that you may get after completing a certain step, it is not the overall solution to the question. Be sure you are answering the question that is being asked.

Incorrect. [[snippet]] Double-check your calculations. A small error along the way will result in an incorrect final solution.

10º

11º

23º

67º

79º