In the following figure, a transversal cuts two parallel lines l and m at
points G and H respectively and the angles thus formed are marked. If ∠ 1
is an acute angle, then, which of the following statements is false?
the options are
(а) ∠ 1 + ∠ 2 = 180°
(b) ∠ 2 + ∠ 5 = 180°
(c) ∠ 3 + ∠ 8 = 180°
(d) ∠ 2 + ∠ 6 = 180°
the person whose answer is the best, will be the brainliest and no spamming
Answers
Answer:
(d)
Step-by-step explanation:
Option (d) is false , because <2=<6 and their sum can't be 180°
If <1 is an acute angle , then <2 would be obtuse (greater than 90°)
since <2=<6 , it is also an obtuse angle ...the sum of two obtuse angles (here <2and<6) can't be 180°..
Hope u understood..
Solution :-
from image we can see that, a transversal n cuts two parallel lines l and m at points G and H respectively .
now, checking given options we get,
a)
→ ∠ 1 + ∠ 2 = 180°
- Correct .
- n is a straight line .
- Linear pair angles are supplementry .
b)
→ ∠ 2 + ∠ 5 = 180°
- Correct .
- Both angles are between parallel lines on same side of transversal .
- Interior angles on same side of transversal or consecutive interior angles are equal to supplementry .
c)
→ ∠ 3 + ∠ 8 = 180°
- Correct .
- Both angles are between parallel lines on same side of transversal .
- Interior angles on same side of transversal or consecutive interior angles are equal to supplementry .
d)
→ ∠ 2 + ∠ 6 = 180°
- False .
- given that, ∠1 is an acute angle .
- So, ∠2 is an obtuse angle .
- ∠ 2 = ∠ 6 { Corresponding angles }
- ∠ 2 + ∠ 6 = 180° only if transversal perpendicularly intersects both parallel lines .
Hence, STATEMENT (d) is false .
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