QuestionAOB and COD are intersecting lines. Find the measure of ∠𝑔.Responses223°223 degrees133°133 degrees43°43 degrees

1. Break Down the Problem

We need to determine the measure of angle $\angle g$ formed by the intersecting lines AOB and COD.

2. Relevant Concepts

• When two lines intersect, they form two pairs of opposite (or vertical) angles.
• The measure of vertical angles is always equal.
• The sum of angles around a point is $360^\circ$.

3. Analysis and Detail

Let:

• $\angle AOB = x$
• $\angle COD = y$

Since these angles are formed by the intersection of lines, we know: $x + y = 180^\circ$ (since they form linear pairs)

Also, if $\angle g$ is vertically opposite to one of the angles, then: $\angle g = x \text{ or } y$

Assuming we are checking the given responses:

• If $\angle g = 223^\circ$, this cannot be true as angles can't exceed $180^\circ$ in this context.
• If $\angle g = 133^\circ$, it is plausible since $\angle COD$ could be $47^\circ$ (making them linear pairs).
• $43^\circ$ also makes sense if paired with angles summing to $180^\circ$.

4. Verify and Summarize

Given the possible options and understanding of linear pairs:

• If $\angle g = 133^\circ$, then the adjacent angle would be $47^\circ$ (since $180^\circ - 133^\circ = 47^\circ$). This satisfies our equation.

The other responses for $223^\circ$ are incorrect, and while $43^\circ$ could be a valid calculation as a linear pair, it does not align neatly with vertical angles.

Final Answer

The measure of $\angle g$ is $133^\circ$.