Question
If the interior angle of point A in this parallelogram measures 155 degrees, what is the interior angel measure of point C?
Answers
Answered by
GPT-4o mini
In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (they add up to 180 degrees).
Given that the angle at point A measures 155 degrees, the opposite angle at point C will also measure 155 degrees.
Since angles A and B are adjacent, we can find the measure of angle B using the following relationship:
\[
\text{Angle A} + \text{Angle B} = 180^\circ
\]
Substituting the value of angle A:
\[
155^\circ + \text{Angle B} = 180^\circ
\]
Now, solving for angle B:
\[
\text{Angle B} = 180^\circ - 155^\circ = 25^\circ
\]
Thus, we find that angle B measures 25 degrees, and therefore, angle D (which is opposite angle B) also measures 25 degrees.
To summarize:
- Angle A = 155 degrees
- Angle B = 25 degrees
- Angle C = 155 degrees (opposite angle A)
- Angle D = 25 degrees (opposite angle B)
Therefore, the interior angle measure of point C is **155 degrees**.
Given that the angle at point A measures 155 degrees, the opposite angle at point C will also measure 155 degrees.
Since angles A and B are adjacent, we can find the measure of angle B using the following relationship:
\[
\text{Angle A} + \text{Angle B} = 180^\circ
\]
Substituting the value of angle A:
\[
155^\circ + \text{Angle B} = 180^\circ
\]
Now, solving for angle B:
\[
\text{Angle B} = 180^\circ - 155^\circ = 25^\circ
\]
Thus, we find that angle B measures 25 degrees, and therefore, angle D (which is opposite angle B) also measures 25 degrees.
To summarize:
- Angle A = 155 degrees
- Angle B = 25 degrees
- Angle C = 155 degrees (opposite angle A)
- Angle D = 25 degrees (opposite angle B)
Therefore, the interior angle measure of point C is **155 degrees**.