Question

If AB=4 feet & AD=10 feet & m What is DC?
What is BD?
What is m What is m

Answer 1

1. DC = AB = 4 ft

2. BD = 10.80 ft

3. m<CED =
`90^(0)`

4. m<EBC =
`65^(o)`

Explanation:

From the given quadrilateral,

Given: AB = 4 ft, AD = 10 ft and m<BAE = 65.

1. DC = AB = 4 ft (opposite sides of a parallelogram are equal)

2. Applying the Pythagoras theorem to ΔABD, we have;

`/hyp/^(2)` =
`/Adj 1/^(2)` +
`/Adj 2/^(2)`

`BD^(2)` =
`4^(2)` +
`10^(2)`

= 16 + 100

= 116

BD =
`√(116)`

= 10.7703

BD = 10.80 ft

3. m<CED =
`90^(0)` (the diagonals bisects each other at right angle)

4. m<ABC + m<BAC + m<ACB = 180

90 + 65 + m<ACB = 180

m<ACB = 180 - 155

m<ACB =
`25^(0)`

So that,

m<BEC + m<EBC + m<ECB = 180

90 + m<EBC + 25 = 180

m<EBC = 180 - 115

m<EBC =
`65^(o)`