Question

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

Answer 1

1). Option (A)

2). Option (D)

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.