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In the given figure, what are the respective measures of ∠BAE and ∠CAD?

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10° and 35°

10° and 45°

35° and 35°

45° and 45°

answer is D.

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Detailed Solution

It is given that AD = AE.

We know that angles opposite to the equal sides are equal.

∴∠ADE = ∠AED

∴ ∠ADE = ∠ADC = 85º …(i)

In ΔABE,

∠ABF = ∠BAE + ∠AEB [Exterior angle property]

∴ ∠BAE = 130º − 85º = 45º

Now in ΔADC,

∠ADC + ∠ACD + ∠CAD = 180º [Angle sum property of a triangle]

⇒ 85º + 50º + ∠CAD = 180º

⇒ ∠CAD = 180º − 85º − 50º

⇒ ∠CAD = 45º

Thus, the respective measures of ∠BAE and ∠CAD are 45º and 45º.

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