Question

In the figure, AB || CD then complete the following activity to find the measure of ∠PDC an ∠CPD.​

Answer 1

$answer$

Given ∠APC=100° ,∠DAB=56°

From the figure,∠APD=180° [Straight angle]------(1)

Now∠APD=∠APC+∠CPD−−−−−−(2)

From (1) & (2), ∠APC+∠CPD=180°

⇒∠CPD=180° −100°

⇒∠CPD=80°

Given AB∥CD&AD be the transversal

∠DAB=∠ADC=56°

[Alternate Angle]

In△PCD,∠CPD+∠PCD+∠PDC=180°

⇒∠PCD=180−80−56[∠PDC=∠ADC]

⇒∠PCD=180−136

⇒∠PCD=44°