Answer:
1)
2)
Step-by-step explanation:
1)
The two triangles are similar by AA similarity.
That means .
We can add to both sides to get .
We can then subtract from both sides to get .
We know that the because they both lie on a straight line.
We can plug in for to get .
We can divide both sides of the equation by to get .
We then add to both sides to get .
So, and we're done!
2)
Because the two bases of a trapezoid are parallel, meaning adjacent top and bottom angles sum to , we have that .
We can subtract a and an from both sides to get .
We then divide both sides of the equation by to get .
We do the same thing for . On the other side of the trapezoid, we have that .
We combine like terms on the left side to get .
We subtract a from both sides to get .
We divide both sides of the equation to get .
So, and we're done!
X - the percent of increase
The percent of increase is approximately 23.8%.
-2y=11-x
-7x+11-x=-13
-8x=-24
x=3
-2y=11-3
-2y=8
y=-4
Answer:
34
Step-by-step explanation:
The triangle with the 28 degree angle is an isosceles as it has 2 sides which are the same length. This means the other angle opposite to one of the sides that is the same length is also 28. The sum of all the angles in the triangle is 180. To find the 3rd angle we just add the two 28 degree angles and subtract it from 180. 180-56=124. The angle of 124 is on a straight line which is divided by another line. The other side of the lines angle will be 180-124 as the angle of a straight line is 180 degrees. 180-124=56. Now we have two angles in the triangle which contains x, 90 degrees and 56 degrees. Once more the total of all angles in the triangle is 180 so subtract the other two angles to get x, 180-(90+56)=34.