Q22. - Algebra 2

Question

Compare the quantity in Column A and the quantity in Column B. Then determine whether:

A. The quantity in Column A is greater.

B. The quantity in Column B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

Step-by-Step Solution

Answer

The two quantities are equal. Therefore, the option C is correct.

Step 1 ­- Label the given diagram.

The labelled diagram is:

Step 2 ­- Description of step.

From the diagram it can be noticed that the angles $\angle AGE$ and $\angle AGH$ forms the linear pair.

Therefore, the sum of the angles $\angle AGE$and $\angle AGH$ is $180°$.

Therefore, it can be obtained that:

$\begin{array}{c}\angle AGE+\angle AGH=180°\\ 120°+\angle AGH=180°\\ \angle AGH=180°-120°\\ \angle AGH=60°\end{array}$

Therefore, the measure of the angle $\angle AGH$ is $180°$.

Step 3 ­- Description of step.

From the diagram it can also be noticed that the angles $\angle AGH$ and $\angle CHF$ forms the corresponding angles as the lines $l$ and m are parallel to each other.

Therefore, the measure of the angles $\angle AGH$ and $\angle CHF$ are equal.

Therefore, it can be obtained that:

$\begin{array}{c}\angle CHF=\angle AGH\\ a°=60°\\ \Rightarrow a=60\end{array}$

Therefore, the value of $a$ is 60.

Now, the value of $2a$ is:

$\begin{array}{c}2a=2\left(60\right)\\ =120\end{array}$

Therefore, the value of $2a$ is 120.

Step 4 ­- Description of step.

The column A has entry 120 and the column B has entry $2a$.

As it has been obtained that $2a=120$.

Therefore, the two quantities in the column A and B are equal.

Therefore, the option C is correct.