In Fig. 5.52, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and ∠CDE.
Solution:
Given, AE || GF || BD and AB || CG || DF
Also, ∠CHE = 120°.
We have to find the measures of ∠ABC and ∠CDE.
Considering BD || AE with CG as transversal,
If two parallel lines are intersected by a transversal, each pair of alternate interior angles is equal.
So, ∠BCH = ∠EHC
From the figure,
∠EHC = 120°
So, ∠BCH = 120°
Considering CG || DF with BD as transversal,
If two parallel lines are intersected by a transversal, each pair of corresponding angles is equal.
So, ∠BCH = ∠CDE
From the figure,
∠BCH = 120°
So, ∠CDE = 120°
Considering AB || CG with BC as transversal,
If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.
So, ∠ABC + ∠BCH = 180°
∠ABC + 120° = 180°
∠ABC = 180° - 120°
∠ABC = 60°
Therefore, the measures of ∠ABC and ∠CDE are 60° and 120°.
✦ Try This: Find all the pairs of supplementary angles.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 99
In Fig. 5.52, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and ∠CDE.
Summary:
In Fig. 5.52, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. The measure of ∠ABC and ∠CDE are 60° and 120°.
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