Answer:
<CPE= 137
Step-by-step explanation:
In order to find the measure of (<CPE), one must add the measure of <(CPD) and (<DPE). From the given picture, one can infer that line (CA) is a diameter. This means that the sum of all angles on either side of the line is (180). Therefore, to find the measure of (<DPE) add up all of the angle measures on one side of the line, and set it equal to (180). Solve and then add the result to the value of (<CPD) to find the measure of (<CPE).
(<CPD) + (<DPE) + (<EPA) = 180
Substitute,
88 + (<DPE) + 43 = 180
Simplify,
131 + (<DPE) = 180
Inverse operations,
<DPE = 49
Now add the value of (<DPE) to (<CPD),
(<CPD) + (<DPE)
= 88 + 49
= 137
