Question

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

Answer 1

x =42

q = 135°

p + q + r = 225°

Explanation:

a)

Since, AB and BC are perpendicular lines.

`m\angle ABC = 90\degree \\</p><p>\therefore 24\degree + x\degree + 24\degree = 90\degree \\</p><p>\therefore x\degree + 48\degree = 90\degree \\</p><p>\therefore x\degree = 90\degree - 48\degree \\</p><p>\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><p>p + 135\degree = 180°..(straight\: line \: \angle' s) \\</p><p>p = 180\degree - 135\degree \\</p><p>\huge \purple {\boxed {p = 45\degree}} \\</p><p>\because r = p ... (vertical \: \angle 's) \\</p><p>\huge \purple {\boxed {r = 45\degree}} \\</p><p>p + q + r = 45\degree + 135\degree + 45\degree \\</p><p>\huge \purple {\boxed {p + q + r = 225\degree }}\\`