Each quadrilateral below is a parallelogram. Find the missing measures

GH = 13

FG = 20

<F = 78

<G = 102

<H = 78

Step-by-step explanation:

Since there are 5 measures that are missing, we will do each one in a different part.

1.  The side length of GH is 13. Since this is a parallelogram, the opposite side of your original side is congruent, meaning that its the same. So, knowing that the opposite of FI is GH, we can say that GH is 13 units long.

2. We can use the same logic for number 2, when finding FG. Since HI is 20. we can say that since the corresponding side is also congruent to our original length, they are equivalent. Basically meaning they are the same

3. a. For finding F, we will need to use a different method. Since a parallelogram is somewhat like a transversal we can use that to our advantage. (If you don't know what a transversal it, look at part B instead) Since we know that angle I is 102, and both line FG and HI are parallel, the angles are basically adjacent, when switched. So we should see that it would have to be 78. Meaning that F is 78.

3. b. If you don't understand what a transversal is, we can still figure it out. Knowing that the figure is a closed shape, along with knowing that its a parallelogram, we can say that if we were to sum the angles F and I, we would get 180. 180-102=78, so F is 78.

4. Since we can use a transversal or just pure logic to say that angle G and I are equivalent, meaning that G is 102.

5. This one is exceptionally simple, just for the fact that we have answered the previous questions. We have H left, which is not only equivalent to F, but using 3. b. we can say that its would only make sense that H is 78 as well, to sum up that half to 180.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.