In kite PQRS, m<QRT = 45 degrees and m<RST = 35 degrees. If RT = 7, find the perimeter of the kite.
Where is the T coming from?
The T is in the middle.
T is actually 90 degrees in the picture of the kite.....
To find the perimeter of the kite, we need to first determine the lengths of the sides of the kite.
In the given kite PQRS, we are provided with the angle measures, m<QRT = 45 degrees and m<RST = 35 degrees. From this, we can conclude that the sum of the angle measures inside a kite is 360 degrees. Therefore, the remaining two angles in the kite are 180 - 45 - 35 = 100 degrees each.
Now, let's focus on triangle RST. We know that the sum of the angle measures in a triangle is 180 degrees. So, the third angle of triangle RST is 180 - 45 - 35 = 100 degrees.
Since we have two angles of the triangle being 100 degrees each, we can conclude that triangle RST is an isosceles triangle. This means that the sides RT and ST are congruent in length. Given that RT = 7, we can say that ST = 7 as well.
Now, let's move to the kite. We know that the opposite sides of a kite are congruent. Therefore, side PQ is congruent in length to side SR, and side QR is congruent in length to side PS.
Since ST = 7, we can conclude that PQ = SR = 7. Similarly, considering triangle QRT, we can determine that QR = PS = 7 as well.
To find the perimeter of the kite, we add up all the side lengths:
Perimeter = PQ + QR + RS + SP
Since all the sides have the same length of 7, the perimeter is:
Perimeter = 7 + 7 + 7 + 7 = 28
Therefore, the perimeter of the kite is 28 units.