In Fig. 5.59, AB||CD. Find the reflex ∠ EFG
Solution:
Given, AB||CD.
We need to find the reflex ∠ EFG.
We can construct a line l, passing through F, which is parallel to both AB and CD.
If two parallel lines are intersected by a transversal, each pair of alternate interior angles are equal.
So, ∠1 = 34°
If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.
∠2 + 135° = 180°
∠2 = 180° - 135°
∠2 = 45°
From the figure,
∠ EFG = ∠1 + ∠2
∠ EFG = 34° + 45°
∠ EFG = 79°
A reflex angle is any angle that is more than 180 degrees (half circle) and less than 360 degrees (full circle).
Now, reflex ∠EFG = 360° - ∠ EFG
reflex ∠EFG = 360° - 79°
reflex ∠EFG = 281°
Therefore, reflex ∠EFG = 281°
✦ Try This: Find all the pairs of supplementary angles from the given figure.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 106
In Fig. 5.59, AB||CD. Find the reflex ∠ EFG
Summary:
AB||CD, reflex ∠EFG = 281°
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