Applying the angle addition theorem, the measure of angle CDF is: 159°.
What is the Angle Addition Theorem?
According to the angle addition theorem, it says that when two smaller angles (e.g. angle 5 and angle 1) make up a larger angle (e.g. angle CDF), then the sum of angle 5 and angle 1 would equal the measure of angle CDF.
We are given the following:
m<5 = 42°
m<1 = 117°
We are asked to find the measure of angle CDF in the image shown below. Thus, we would apply the angle addition theorem as follows:
m<5 + m<1 = m<CDF
Substitute
42 + 117 = m<CDF
159° = m<CDF
m<CDF = 159°
Thus, applying the angle addition theorem, the measure of angle CDF is: 159°.
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