ABCD is a rhombus in which the altitude
from D to side AB bisects AB. Then ZA
and ZB respectively, are
(A) 60°. 120° (B) 120°, 60°
(C) 80°, 100° (D) 100°, 80°
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Answer:
Option(A)
Step-by-step explanation:
In a ΔAED and ΔBED,
DE = DE ( common line)
∠AED = ∠BED
AE = EB
∴ ΔAED ≅ ΔBED
∴ AD = BD
But AD = AB
⇒ AD = AB = BD
∴ ABD is an equilateral traingle.
∴ ∠A = 60°
⇒ ∠A = ∠C = 60°
But Sum of adjacent angles of a rhombus is supplimentary.
∠ABC + ∠BCD = 180°
⇒ ∠ABC + 60°= 180°
⇒ ∠ABC = 180° - 60° = 120°.
∴ ∠ABC = ∠ADC = 120°
∴ Angles of rhombus are ∠A = 60° and ∠B = 120°.
Hence, the answer is Option(A).
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