Question

if m || n and p || q if angle 1 =75 prove that angle 2=angle 1+1/3 of a right angle

Answer 1

Answer:

Given:

m || n    and p || q

m∠1 = 75°

To prove: ∠2 = ∠1 + 1/3 of right angle

Figure is attached.

1/3 of right angle = 1/3 × 90 = 30°

⇒ ∠1 + 30 = 75 + 30 = 105° .....................(1)

From figure,

m || n and p is traversal.

∠1 + x = 180°   ( Sum of the interior angle on the same side of traversal in 180° )

75 + x = 180

x = 180 - 75

x = 105°

∠2 = x = 105°  ( corresponding angles of parallel line p & q ) .............(2)

From (1) and (2)

∠2 = ∠1 + 1/3 of right angle

Hence proved.

Answer 2

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