Question

ABCD is a quadrilateral.

Sides are extended as shown.


Show that x = 100°

Answer 1

Given :

ABCD is a quadrilateral.

Angle ADC = 90 degree

Angle DCB = 120 degree

Now angle DAB = 70 degree (alternate angles)

We know that the interior angles of a quadrilateral is 360 degrees.

So,

∠ DAB + ∠ ABC + ∠ BCD + ∠ CDA = 360°

70° + ∠ ABC + 120° + 90 ° = 360°

∠ ABC = 360° - (70° + 120° + 90°)

∠ ABC = 360° - 280°

∠ ABC = 80°

Now ∠ x = 180° - ∠ ABC (Line AB extended is 180° )

= 180° - 80°

= 100°

Hence proved.