Question

7. In each of the diagrams, the straight lines

AB and CD intersect at a point. Find the
measure of each unknown marked angle.

Answer 1

The calculated measures of the marked angles are x = 33, y = 147, q = 52 and p = 52

How to determine the measures of the marked angles

From the question, we have the following parameters that can be used in our computation:

The figures

Figure 7(a)

The angle AEC and DEB are vertical angles

So, we have

DEB = AEC

This means that

x = 33

Also, we have the the angles AEC and BEC are on a straight line

So, we have

y + 33 = 180

y = 180 - 33

y = 147

Figure 7(b)

The angles AFC and DFA are on a straight line

So, we have

q + 128 = 180

q = 180 - 128

q = 52

Still using the therem of straight line angles, we have

p + 52 + 76 = 180

p + 128 = 180

This means that

p = 180 - 128

p = 52