An angle bisector divides an angle into two equal halves.
The measure of angle [tex]\angle CPD[/tex] is 70 degrees
The complete question is an illustrates the concept of angle bisector;
Where:
[tex]\angle RPD = 140^o[/tex], and line PC bisects [tex]\angle RPD[/tex]
Because line PC bisects [tex]\angle RPD[/tex], then it means that the measure of RPD is twice the measure of CPD:
So, we have:
[tex]\angle RDP = 2 \times \angle CPD[/tex]
Substitute [tex]\angle RPD = 140^o[/tex]
[tex]140^o = 2 \times \angle CPD[/tex]
Divide both sides by 2
[tex]70^o = \angle CPD[/tex]
Apply symmetric property of equality:
[tex]\angle CPD = 70^o[/tex]
Hence, the measure of angle [tex]\angle CPD[/tex] is 70 degrees
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