In the figure shown,
a
∥
b
a
∥
b
.
The figure shows two diagonal parallel lines. A horizontal line cuts the two diagonal lines at different points. On the intersection point on the left, the angle formed on the top left portion is labeled as 1, the angle formed on the top right portion is labeled as 2, the angle formed on the bottom left portion is labeled as 5, and the angle formed on the bottom right portion is labeled as 6. On the intersection point on the right, the angle formed on the top left portion is labeled as 3, the angle formed on the top right portion is labeled as 4, the angle formed on the bottom left portion is labeled as 7, and the angle formed on the bottom right portion is labeled as 8.
Which angles are supplements of angle 1? Select all that apply.
A.
∠
6
∠
6
B.
∠
2
∠
2
C.
∠
4
∠
4
D.
∠
7
∠
7
E.
∠
3
∠
3
F.
∠
8
∠
8
Well, according to the information given, the angles that are supplements of angle 1 are ∠2 and ∠7. So the correct answers would be B and D. Now, don't go around giving these angles your supplements, they might not be hungry!
To determine which angles are supplements of angle 1, we need to find angles that, when added to angle 1, equal 180 degrees.
Angle 6 is the vertical angle to angle 1, and vertical angles are always equal. So the measure of angle 6 is also equal to the measure of angle 1. Therefore, angle 6 is a supplement of angle 1. So, option (A) ∠6 is a supplement of angle 1.
To check if any other angles are supplements of angle 1, we can look for pairs of angles that form a straight line when added.
Angle 2 forms a straight line with angle 1 across a horizontal line. So, the sum of angle 2 and angle 1 equals 180 degrees. Therefore, angle 2 is a supplement of angle 1. So, option (B) ∠2 is a supplement of angle 1.
No other angles form a straight line with angle 1 or have equal measures to angle 1 across a pair of parallel lines. Therefore, the correct answers are options (A) ∠6 and (B) ∠2.
To determine which angles are supplements of angle 1, we need to know what it means for angles to be supplements.
Two angles are considered supplementary if their sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary, then A + B = 180 degrees.
In the given figure, angle 1 is formed by the intersection of the horizontal line and the diagonal line on the left side.
To find the supplementary angles of angle 1, we need to look for angles that, when added to angle 1, result in a sum of 180 degrees.
From the given figure, we can see that angle 6 is on the same top left portion as angle 1. Since the two diagonal lines are parallel, angle 6 and angle 1 are corresponding angles.
Corresponding angles are congruent, meaning they have the same measure. Therefore, angle 6 is congruent to angle 1. Since they have the same measure, they will also have the same supplement.
So, we can conclude that ∠6 is a supplement of ∠1.
To summarize: ∠6 is a supplement of ∠1.
Therefore, the correct option is (A) ∠6.
hard to say from all the words. But recall that
consecutive angles on the transversal are supplementary
alternate interior angles are congruent
now start marking the angles