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
Answers
Answer:
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.
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