1. Given that ABCD is a rhombus with ∠DBC=49∘, what is ∠DAB? A. 82 degrees
B. 90 degrees
C. 49 degrees
D. 98 degrees

2. In a rhombus FGHJ, m∠JKF=(3y+6)∘ and m∠KFG =(7y−14)∘. Find the value of y?
A. 20
B. 10
C. 8
D. 5

1). Option (A)

2). Option (D)

Step-by-step explanation:

1). We will use two properties of the rhombus,

   - Diagonals of a rhombus are perpendicular and bisect each other.

   - Diagonals of a rhombus bisect the opposite angles.

From the figure attached,

    m∠DBC = 49° [Given]

    m∠DBA = 49° [m∠DBC = m∠DBA]

    In ΔAOB,

    m∠AOB + m∠OBA + m∠BAO = 180° [Triangle sum theorem]

    90°+ 49° + m∠BAO = 180°

    m∠BAO = 41°

    Since, m∠DAB = 2(m∠BAO)

                              = 2(41°)

                              = 82°

Option (A) will be the answer.

2). From the figure attached,

    m∠JKF = (3y + 6)°

    m∠KFG = (7y - 14)°

    Since, m∠JKF ≅ m∠KFG

    (3y + 6) = (7y - 14)

    7y - 3y = 6 + 14

    4y = 20 ⇒ y = 5

    Option (D) will be the answer.

quit

step-by-step explanation:

$2416.6

step-by-step explanation:

per hour = $ 25

total work time = 35

commission = 15%

total she has to make = $ 4,500

let she sold x dollar products

so her commission will be 15 % of x

now

total = weekly basic pay + commission

4500= (25*35) + 15 % of x

4500=875 + * x

4500-875 =   * x

3625= * x

multiplying wwith 100 on both sides gives

36250 = 15 x

now

x =  

x= $2416.6