Question
Ranger draws parallelogram RSTU. If the interior angle measure point S is 95 degree, which statement must be true?
Answers: The interior angle measure of point U is 95 degrees. The interior angle measure of point U is 95 degrees. The interior angle measure of point U is 85 degrees. The interior angle measure of point U is 85 degrees. The interior angle measure of point R is 95 degrees. The interior angle measure of point R is 95 degrees. The measure of the interior angle at point T is 95 degrees. The measure of the interior angle at point T is 95 degrees.
Answers: The interior angle measure of point U is 95 degrees. The interior angle measure of point U is 95 degrees. The interior angle measure of point U is 85 degrees. The interior angle measure of point U is 85 degrees. The interior angle measure of point R is 95 degrees. The interior angle measure of point R is 95 degrees. The measure of the interior angle at point T is 95 degrees. The measure of the interior angle at point T is 95 degrees.
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 interior angle at point S is 95 degrees:
1. The angle at point U (which is opposite to S) must also be 95 degrees.
2. The angle at point R (which is adjacent to S) must be 180 - 95 = 85 degrees.
3. Similarly, the angle at point T (which is adjacent to U) must also be 85 degrees.
So, the statements that must be true are:
- The interior angle measure of point U is 95 degrees. (True)
- The interior angle measure of point R is 85 degrees. (True)
- The interior angle measure of point T is 85 degrees. (True)
The false statements are those claiming that angles U or T are 95 degrees or that angle R is 95 degrees.
Thus, the only true statements based on the given conditions are:
- The interior angle measure of point U is 95 degrees.
- The interior angle measure of point R is 85 degrees.
- The measure of the interior angle at point T is 85 degrees.
Given that the interior angle at point S is 95 degrees:
1. The angle at point U (which is opposite to S) must also be 95 degrees.
2. The angle at point R (which is adjacent to S) must be 180 - 95 = 85 degrees.
3. Similarly, the angle at point T (which is adjacent to U) must also be 85 degrees.
So, the statements that must be true are:
- The interior angle measure of point U is 95 degrees. (True)
- The interior angle measure of point R is 85 degrees. (True)
- The interior angle measure of point T is 85 degrees. (True)
The false statements are those claiming that angles U or T are 95 degrees or that angle R is 95 degrees.
Thus, the only true statements based on the given conditions are:
- The interior angle measure of point U is 95 degrees.
- The interior angle measure of point R is 85 degrees.
- The measure of the interior angle at point T is 85 degrees.