Question

CD and EF are parallel lines. AB is a straight line

Answer 1

Answer:

x =42

q = 135°

p + q + r = 225°

Step-by-step explanation:

a)

Since, AB and BC are perpendicular lines.

$m\angle ABC = 90\degree \\\therefore 24\degree + x\degree + 24\degree = 90\degree \\\therefore x\degree + 48\degree = 90\degree \\\therefore x\degree = 90\degree - 48\degree \\\huge \red {\boxed {\therefore x = 42}}$

b) (i)

Since, CD and EF are parallel lines and AB is a straight line.

$\therefore q = 135\degree... (vertical \: \angle 's) \\\\p + 135\degree = 180°..(straight\: line \: \angle' s) \\p = 180\degree - 135\degree \\\huge \purple {\boxed {p = 45\degree}} \\\because r = p ... (vertical \: \angle 's) \\\huge \purple {\boxed {r = 45\degree}} \\p + q + r = 45\degree + 135\degree + 45\degree \\\huge \purple {\boxed {p + q + r = 225\degree }}$