The figure shows a rhombus ABCD. The diagonal DB is produced to E such that BC = BE and CDE = 46°.
1 answer:
Answer:
(i) 88°
(ii) 23°
Step-by-step explanation:
See the picture below.
The numbers added in red are the angle measures. The numbers added in black are the order in which each angle measure was written.
ABCD is a rhombus, so all sides are congruent.
Triangle BCD is isosceles with sides DC and BC congruent, so <DBC is congruent to <BDC. From the sum of the measures of the angles of a triangle, we get m<DCB. Opposite angles of a rhombus are congruent, so m<A = m<DCB. From the sum of the measures of the angles of a triangle and from isosceles triangle ADB we get m<ADB and m<ABD. From m<DBC and supplementary angles, we get m<CBE. From isosceles triangle BCE, we get m<BCE.
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Answer:
The answer to your question is 10 units
Step-by-step explanation:
Data
A (-3, -1)
B (-3 , 5)
length of a side = 8 units
Process
1.- Calculate the distance between A and B
dAB =
x1 = -3 y1 = -1
x2 = -3 y2 = 5
-Substitution
dAB =
dAB =
dAB =
dAB = 6 u
2.- Calculate the diagonal using the Pythagorean theorem.
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = 10 units
- Conclusion
The diagonal of the rectangle measures 10 units