In the given figure AB∥DC and AD∥BC If ∠ABC=75∘ then ∠C
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In the given figure, AB∥DC and AD∥BC. If ∠ABC=75∘, then ∠CDA = ___.
A. 105∘
B. 30∘
C. 75∘
D. 60∘
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
In △ABC and △CDA,
(i) ∠BAC = ∠DCA ....(alternate angles)
(ii) AC = AC .......(common)
(iii) ∠BCA=∠DAC .....(alternate angles)
∴ △ABC≅△CDA .....(ASA Postulate)
⇒∠ABC = ∠CDA .......(CPCT)
∴ If ∠ABC = 75∘, then ∠CDA = 75∘.
