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 = 180
2(∢A) + 80 < 180 , (remember angle A = angle C)
∢A < 50°
Shouldn't the sum of the interior angles of a quadrilateral be 360 degrees?
Of course drwls is right, how silly of me
so 2(∢A) + 80 < 360
∢A < 140°
To find the largest possible size for angle A or C in kite ABCD, we need to understand some properties of kites.
Here are the key properties of a kite:
1. Two pairs of adjacent sides are congruent (AB=BC and AD=DC).
2. The diagonals are perpendicular and intersect each other at right angles (AC and BD).
In a kite, the sum of the measures of any two opposite angles is always 180 degrees. Therefore, the sum of angles A and C must be 180 - 80 = 100 degrees.
To find the largest size for angles A or C, we need to consider the location of angle B. Since angle B is at the top of the kite and measures 80 degrees, it means that one of angles A or C is adjacent to angle B, while the other angle is opposite to angle B.
Since angle A is opposite to angle B, it can be the largest angle, while angle C, being adjacent to angle B, must be smaller. Therefore, we can conclude that the largest possible size for angle A is 100 degrees.
So, the largest possible size for angle A or C in kite ABCD is 100 degrees.