Answer:
Part 1) [tex]AC=40\ units[/tex]
Part 2) [tex]DC=29\ units[/tex]
Part 3) [tex]m\angle ABE=39^o[/tex]
Part 4) [tex]m\angle BCE=51^o[/tex]
Step-by-step explanation:
we know that
A kite has two pairs of consecutive, congruent sides the diagonals are perpendicular and the non-vertex angles are congruent
Part 1) Find AC
we know that
BD is the axis of symmetry, bisects the diagonal AC
so
[tex]AE=EC[/tex]
we have
[tex]EC=20\ units[/tex]
[tex]AC=AE+EC[/tex] ----> by segment addition postulate
therefore
[tex]AC=20+20=40\ units[/tex]
Part 2) Find CD
we know that
CDE is a right triangle (the diagonals are perpendicular)
so
Applying Pythagorean Theorem
[tex]DC^2=EC^2+ED^2[/tex]
substitute the values
[tex]DC^2=20^2+21^2[/tex]
[tex]DC^2=841\\DC=29\ units[/tex]
Part 3) Find m∠ABE
we know that
In the right triangle ABE
[tex]51^o+m\angle ABE=90^o[/tex] ----> by complementary angles
[tex]m\angle ABE=90^o-51^o=39^o[/tex]
Part 4) Find m∠BCE
we know that
[tex]m\angle BCE=m\angle BAE[/tex] ----> diagonal BD is the axis of symmetry
we have
[tex]m\angle BAE=51^o[/tex]
therefore
[tex]m\angle BCE=51^o[/tex]
The measure of AC is 40 units.
The measure of the length DC is 29 units.
The measure of the angle ABE is 39 degrees.
The measure of the angle BCE is 51 degrees.
The missing lengths and angle measures in kite ABCD.
According to the question
The rhombus is a four-sided quadrilateral with all its four sides equal in length.
Rhombus is a kite with all its four sides congruent.
A kite is a special quadrilateral with two pairs of equal adjacent sides.
1. The measure of the length of AC is;
In the figure, BD is the axis of symmetry, bisects the diagonal AC.
Then,
[tex]\rm AE = EC[/tex]
And the measure of AC is,
[tex]\rm AC = AE+EC \\ \\ AC = 20+20 \\ \\ AC = 40 \ units[/tex]
The measure of AC is 40 units.
2. In the figure, CDE is a right triangle (the diagonals are perpendicular)
Then,
By applying the Pythagoras Theorem
[tex]\rm DC^2=EC^2+ED^2\\ \\ DC^2=20^2+21^2\\\\ DC^2 = 400+441 \\ \\ DC^2 = 841\\ \\ DC = 29 \ \rm units[/tex]
The measure of the length DC is 29 units.
3. In the right triangle ABE by the complementary angles;
[tex]\rm 51+ \angle ABE = 90\\ \\ \angle ABE=90-51\\ \\ \angle ABE=39 \ degrees[/tex]
The measure of the angle ABE is 39 degrees.
4. By the axis of symmetry the diagonal BD is;
[tex]\rm m \angle BCE = m \angle BAE\\\\ m \angle BCE = m \angle BAE = 51 \ degrees[/tex]
The measure of the angle BCE is 51 degrees.
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https://brainly.com/question/11089614