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Question
In a parallelogram ABCD, ∠B = 105°. Determine the measure of ∠A and ∠D.
Solution
Given: ∠B = 105°.
We know that the sum of any two successive parallelogram angles is 180°.
∴ ∠A + ∠B = 180°
⇒ ∠A + 105° = 180°
⇒ ∠A = 180° – 105°
= 75°
Also, ∠A + ∠D = 180°
⇒ 75 + ∠D = 180°
⇒ ∠D = 180° – 75°
= 105°
Hence, ∠A = 75° and ∠D = 105°.
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