Answer:
[tex]CPD = 80[/tex]
[tex]PCD = 44[/tex]
Explanation:
Given
[tex]AB || CD[/tex]
[tex]BAD = 56[/tex]
[tex]CPA = 100[/tex]
See attachment
Required
Determine PCD and CPD
First, we need to calculate CPD
Since DPA is a straight line and CPA = 100;
We have that:
[tex]CPA + CPD = 180[/tex] --- angle on a straight theorem
Substitute 100 for CPA
[tex]100 + CPD = 180[/tex]
Subtract 100 from both sides
[tex]100-100 + CPD = 180-100[/tex]
[tex]CPD = 80[/tex]
Next, we calculate PCD
We have that:
[tex]DAB= ADC = 56[/tex] --alternate angle
In triangle PCD
[tex]PCD + CPD + PDC = 180[/tex] --- angles in a triangle
Where
[tex]PDC = ADC = 56[/tex]
So, we have:
[tex]PCD +80 + 56 = 180[/tex]
[tex]PCD +136 = 180[/tex]
Subtract 136 from both sides
[tex]PCD = 180 - 136[/tex]
[tex]PCD = 44[/tex]
