Answer:
Both angles x and y are 69 degrees
Step-by-step explanation:
Because the angle with measure 69 degrees and angle x are alternate interior angles, they have equal value. Therefore, x has measure 69 degrees. Because this figure is a trapezoid, angle y is supplementary to the angle with measure 111 degrees. Therefore, y=180-111=69 degrees as well. Hope this helps!
Answer:
3,000 meters
Step-by-step explanation:
recall that 1 kilometer = 1,000 meters
hence
3 kilometers = 1,000 meters x 3 = 3,000 meters
Answer:
x = 27, and y = 47.
Step-by-step explanation:
AB is a line, so the measures of the angles measuring
2x + 1, 3x + 10, and 8/9 x + 10
add to 180 degrees. We can use that fact to find x.
2x + 1 + 3x + 10 + 8/9 x + 10 = 180
Add like terms on the left side except for the faction.
5x + 8/9 x + 21 = 180
Multiply both sides by 9.
45x + 8x + 189 = 1620
Add like terms on the left side. Subtract 168 from both sides.
53x = 1431
Divide both sides by 53.
x = 27
The angle measuring 3x + 10 is vertical with the angle that is made up of the measures y - 3 and y. Therefore, the sum of the measures y - 3 and y equals the measure 3x + 10. We know x, so we can find 3x + 10.
3x + 10 = 3(27) + 10 = 91
Now we set the sum of y - 3 and y equal to 91 and solve for y.
y - 3 + y = 91
2y - 3 = 91
2y = 94
y = 47
x = 27, and y = 47.
Answer:
1 and 9
Step-by-step explanation:
By the Triangle Inequality Theorem, the sum of two side lengths of a triangle is always greater than the length of the third side.
In other words, in a triangle with side lengths 
and 
we always have 
Applying this to this question, the other side length, 
must satisfy the following inequalities:
Solving these inequalities gives
Combining these solutions, we have 
Therefore, the length of the third side falls between 1 and 9.
