what do you need to know to solve this? you have kite ABCD. angle B is at the top of the kite and measures 80 degrees. angles A and C are on the sides and angle D is at the bottom of the kite. what is the largest siza that angle A or C could be?
Imagine a "very large" kite so that D is many km below A.
Then angle D would approach 0°
and
angle A + angle C + "almost zero" + 80 = 360
2(∢A) + 80 < 360 , (remember angle A = angle C)
∢A < 140°
dees nuts
To find the largest possible size for angle A or C in the given kite ABCD, we need to apply the property of the angles in a kite.
In a kite, the two pairs of consecutive angles (angles that share a side) are congruent, meaning they have the same measure.
Given that angle B measures 80 degrees, we can determine the largest possible size for angle A or C by making the other pair of consecutive angles as small as possible.
Since angle B is at the top of the kite, angle D is at the bottom. Therefore, angle A and angle C are the pair of consecutive angles we need to consider.
To make angle A or C as large as possible, we need to make the other angle of the pair as small as possible. This happens when angle D is as small as possible.
In a kite, the sum of angle D and angle B is always 180 degrees. Therefore, angle D would measure 180 - 80 = 100 degrees to be as small as possible.
Now, to find the largest possible size for angle A or C, we can use the property of the consecutive angles in a kite. Since the sum of the consecutive angles is always 180 degrees, we subtract the known measure of angle D (100 degrees) from 180.
180 - 100 = 80 degrees
Hence, the largest possible size for angle A or C in the given kite ABCD is 80 degrees.