Question

plz answer this question right now plz its urgent.

Answer 1

Hey there !

Thanks for the question !

Here's the answer !

Q1. Given that ABCD is a parallelogram.

Properties of Parallelogram :

• They have equal opposite angles.

• They have adjacent supplementary angles

This implies that, ∠ A = ∠ C and ∠ A + ∠ B = 180°.

Given that, ∠ A = 72°

⇒ ∠ C = 72°

Also, ∠ B = 180° - ∠ A

⇒ ∠ B = 180° - 72°

⇒ ∠ B = 108° = ∠ D.

So the measures are: ∠ B = ∠ D = 108° ; ∠C = 72°.

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Q2. Consider Δ BDC

∠ A = ∠ C ( Opposite Angle of Parallelogram )

=> ∠ C = 80°

Now applying Angle Sum property for Δ BDC, we get,

=> 60 + 80 + ∠ CDB = 180°

=> 140 + ∠ CDB = 180°

=> ∠ CDB = 180 - 140 = 40°

Considering AB ║ DC, BD as the transversal we get that,

∠ CBD = ∠ ADB ( Alternate Angles )

=> ∠ ADB = 60°.

Hope my answer helped !