Question
Figure LMNO is a parallelogram.
A parallelogram has points on each corner. The points are M, N, O, L going from the top left, clockwise.
Angles L and M are supplementary. What is the sum of their measures?
The sum of the measures of angles L and M is ___°.
Lines DE and AB intersect at point C.
Lines D E and A B intersect at point C. Angle A C E is (2 x + 2) degrees. Angle E C B is (5 x + 3) degrees.
What is the value of x?
12
25
38
52
Triangle ABC is a right triangle.
Triangle A B C is a right triangle. Angle A C B is 90 degrees, angle C B A is 31 degrees, and angle B A C is 59 degrees.
What is the relationship between angles A and B?
They are congruent.
They are complementary.
They are supplementary.
There is no relationship between them.
Angles 1 and 2 form a right angle.
2 lines form a right angle. Another line extends between the 2 lines to form 2 angles. The top angle is labeled 1, and the bottom angle is labeled 2.
Which word describes their measures?
linear
congruent
complementary
supplementary
Given: Line A B intersects Line D E at point C.
Prove: AngleDCB Is-congruent-toAngleECA
Line D E intersects line B A at point C.
A 2-column table with 6 rows. Column 1 is labeled statements with the entries line A B intersects line D E at point C, angle D C B and angle B C E are a linear pair, angle D C B is supplementary to angle B C E, angle B C E and angle E C A are a linear pair, angle B C E is supplementary to angle E C A, angle D C B is-congruent-to angle E C A. Column 2 is labeled reasons with the entries given, definition of linear pair, linear pair post, definition of linear pair, question mark, congruent to supplementary theorem.
What is the missing reason in step 5?
linear pair postulate
given
definition of complementary angles
congruent complements theorem
A parallelogram has points on each corner. The points are M, N, O, L going from the top left, clockwise.
Angles L and M are supplementary. What is the sum of their measures?
The sum of the measures of angles L and M is ___°.
Lines DE and AB intersect at point C.
Lines D E and A B intersect at point C. Angle A C E is (2 x + 2) degrees. Angle E C B is (5 x + 3) degrees.
What is the value of x?
12
25
38
52
Triangle ABC is a right triangle.
Triangle A B C is a right triangle. Angle A C B is 90 degrees, angle C B A is 31 degrees, and angle B A C is 59 degrees.
What is the relationship between angles A and B?
They are congruent.
They are complementary.
They are supplementary.
There is no relationship between them.
Angles 1 and 2 form a right angle.
2 lines form a right angle. Another line extends between the 2 lines to form 2 angles. The top angle is labeled 1, and the bottom angle is labeled 2.
Which word describes their measures?
linear
congruent
complementary
supplementary
Given: Line A B intersects Line D E at point C.
Prove: AngleDCB Is-congruent-toAngleECA
Line D E intersects line B A at point C.
A 2-column table with 6 rows. Column 1 is labeled statements with the entries line A B intersects line D E at point C, angle D C B and angle B C E are a linear pair, angle D C B is supplementary to angle B C E, angle B C E and angle E C A are a linear pair, angle B C E is supplementary to angle E C A, angle D C B is-congruent-to angle E C A. Column 2 is labeled reasons with the entries given, definition of linear pair, linear pair post, definition of linear pair, question mark, congruent to supplementary theorem.
What is the missing reason in step 5?
linear pair postulate
given
definition of complementary angles
congruent complements theorem
Answers
GPT-4o mini
Let's address each of your questions one by one.
1. **Sum of Angles L and M in Parallelogram:**
Angles L and M are supplementary, meaning they add up to 180 degrees. Therefore, the sum of their measures is **180°**.
2. **Finding the value of x:**
We know that angles A C E and E C B are vertical angles. Therefore, they are equal:
\[
2x + 2 = 5x + 3.
\]
Now solve for x:
\[
2 = 3x + 3,
\]
\[
-1 = 3x,
\]
\[
x = -\frac{1}{3}.
\]
Since this result does not match any of the possible answers you've provided, it seems there may be an error in the interpretation of angles. Please check that the angles are set up correctly for the relationship.
3. **Relationship Between Angles A and B in Triangle ABC:**
In triangle ABC, since it is a right triangle:
- Angle A + Angle B + Angle C = 180°.
- Given angle C is 90°, Angle A + Angle B = 90°.
- Therefore, Angles A and B are **complementary**.
4. **Describing the Measures of Angles 1 and 2:**
Since angles 1 and 2 form a right angle (which measures 90 degrees), they are **complementary**.
5. **Missing Reason in Proof for Angle DCB and Angle ECA:**
The missing reason in step 5 should relate to how Angle BCE is supplementary to Angle ECA due to being part of a linear pair. Therefore, the correct option is **congruent complements theorem**.
If there are any further clarifications or other questions, feel free to ask!
1. **Sum of Angles L and M in Parallelogram:**
Angles L and M are supplementary, meaning they add up to 180 degrees. Therefore, the sum of their measures is **180°**.
2. **Finding the value of x:**
We know that angles A C E and E C B are vertical angles. Therefore, they are equal:
\[
2x + 2 = 5x + 3.
\]
Now solve for x:
\[
2 = 3x + 3,
\]
\[
-1 = 3x,
\]
\[
x = -\frac{1}{3}.
\]
Since this result does not match any of the possible answers you've provided, it seems there may be an error in the interpretation of angles. Please check that the angles are set up correctly for the relationship.
3. **Relationship Between Angles A and B in Triangle ABC:**
In triangle ABC, since it is a right triangle:
- Angle A + Angle B + Angle C = 180°.
- Given angle C is 90°, Angle A + Angle B = 90°.
- Therefore, Angles A and B are **complementary**.
4. **Describing the Measures of Angles 1 and 2:**
Since angles 1 and 2 form a right angle (which measures 90 degrees), they are **complementary**.
5. **Missing Reason in Proof for Angle DCB and Angle ECA:**
The missing reason in step 5 should relate to how Angle BCE is supplementary to Angle ECA due to being part of a linear pair. Therefore, the correct option is **congruent complements theorem**.
If there are any further clarifications or other questions, feel free to ask!