Part (a)
Answer: 42
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Work Shown:
The angle ABC is 90 degrees since AB and BC are perpendicular. The two segments form a right angle. Therefore, the three pieces of the angle must add to 90
24+x+24 = 90
x+48 = 90
x+48-48 = 90-48 ... subtracting 48 from both sides
x = 42
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Part (b), subpart (i)
Angle q is congruent to the 135 degree angle because they are vertical angles.
Vertical angles are opposite angles formed by the X shape when two lines cross, and vertical angles are always the same measure.
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Part (b), subpart (ii)
Answer: 225
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Reasoning:
The four angles p,q,r and the 135 all add to 360, so,
p+q+r+135 = 360
subtract 135 from both sides so we isolate the "p+q+r" and that leads to
p+q+r+135 = 360
p+q+r+135-135 = 360-135
p+q+r = 225