Let the angles be x and (180-x).
Let 2x = 180-x.
Then 3x = 180, and x = 60. One angle is 60 degrees and the other is 180-60, or 120, degrees.
Answer:
The statement is false.
Step-by-step explanation:
A parallelogram is a figure of four sides, such that opposite sides are parallel
A rectangle is a four-sided figure such that all internal angles are 90°
Here, the statement is:
"A rectangle is sometimes a parallelogram but a parallelogram is always a
rectangle."
Here if we found a parallelogram that is not a rectangle, then that is enough to prove that the statement is false.
The counterexample is a rhombus, which is a parallelogram that has two internal angles smaller than 90° and two internal angles larger than 90°, then this parallelogram is not a rectangle, then the statement is false.
The correct statement would be:
"A parallelogram is sometimes a rectangle, but a rectangle is always a parallelogram"
Answer:
0.5 hour
Step-by-step explanation:
Given
Speed of Dina = 10 km/h
Distance = 20 km
So the time Dina taken to complete the track is:
![Speed=\frac{distance}{time}\\10=\frac{20}{time}\\time=\frac{20}{10}\\ time=2\ hours](https://tex.z-dn.net/?f=Speed%3D%5Cfrac%7Bdistance%7D%7Btime%7D%5C%5C10%3D%5Cfrac%7B20%7D%7Btime%7D%5C%5Ctime%3D%5Cfrac%7B20%7D%7B10%7D%5C%5C%20time%3D2%5C%20hours)
The time taken by Dina is 2 hours. As masha started with dina but she was 4 km of the path left to cycle,
her distance covered in 2 hours was:
![Distance\ covered\ by\ Masha\ in\ 2\ hours=20-4\\=16 km](https://tex.z-dn.net/?f=Distance%5C%20covered%5C%20by%5C%20Masha%5C%20in%5C%202%5C%20hours%3D20-4%5C%5C%3D16%20km)
So we know the time and distance:
Now,
![Speed\ of\ Masha=\frac{distance}{time}\\ =\frac{16}{2}\\ =8\ kilometer\ per\ hour](https://tex.z-dn.net/?f=Speed%5C%20of%5C%20Masha%3D%5Cfrac%7Bdistance%7D%7Btime%7D%5C%5C%20%3D%5Cfrac%7B16%7D%7B2%7D%5C%5C%20%3D8%5C%20kilometer%5C%20per%5C%20hour)
We have to calculate the time that will be needed by MAsha to complete the track:
As we know the speed and remaining distance
![Speed=\frac{distance}{time}\\8=\frac{4}{time}\\ time=\frac{4}{8}\\time=0.5\ hours](https://tex.z-dn.net/?f=Speed%3D%5Cfrac%7Bdistance%7D%7Btime%7D%5C%5C8%3D%5Cfrac%7B4%7D%7Btime%7D%5C%5C%20time%3D%5Cfrac%7B4%7D%7B8%7D%5C%5Ctime%3D0.5%5C%20hours)
Masha needs 0.5 hour to complete the track ..